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Common Core: High School - Algebra : Reasoning with Equations & Inequalities

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Example Question #51 : Reasoning With Equations & Inequalities

Solve the following by completing the square. Round your answer to the nearest hundredth:

$x^{2} + 19 x - 52 = 0$

Possible Answers:

x = 2.43 , x = -21.43

x = -0.06, x = -18.93

x = 1.93, x = -20.93

x = -5.2, x = -7.4

x = -3.38, x = 7.28

Correct answer:

x = 2.43 , x = -21.43

Explanation:

The first step is to add to both sides.

$x^{2} + 19 x - 52 + 52 = 0 + 52$

$x^{2} + 19 x = 52$

Now we take the coefficient in front of the $\uptext{x}$ term, divide it by , square it and add it to each side.

$x^{2} + 19 x + \frac{19}{2} ^2 = 52 + \frac{19}{2} ^2$

$x^{2} + 19 x + \frac{361}{4} = 52 + \frac{361}{4}$

Now we factor the left hand side, and add up the right hand side.

$\left( x + \frac{19}{2} \right)^2= \frac{569}{4}$

Now we take the square root of each side.

$\sqrt{\left( x + \frac{19}{2} \right)^2}= \sqrt{ \frac{569}{4} }$

$x + \frac{19}{2} = \sqrt{ \frac{569}{4} }$

Now we subtract $\frac{19}{2}$ from each side.

$x + \frac{19}{2} - \frac{19}{2} = \sqrt{ \frac{569}{4} }- \frac{19}{2}$

$x = - \frac{19}{2} + \frac{\sqrt{569}}{2}$

Since we are taking the square root, we need to set up equations to solve for $\uptext{x}$ .

$x = - \frac{19}{2} + \frac{\sqrt{569}}{2}$

x = 2.43

$x = - \frac{\sqrt{569}}{2} - \frac{19}{2}$

x = -21.43

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Example Question #1 : Solve Quadratic Equations By Inspection, Quadratic Formula, Factoring, Completing The Square, And Taking Square Roots: Ccss.Math.Content.Hsa Rei.B.4b

Solve $- 11 x^{2} + 20 x - 44 = 0$

Possible Answers:

$x = \frac{120}{11} - \frac{8 i}{11} \sqrt{6} , x = - \frac{100}{11} + \frac{8 i}{11} \sqrt{6}$

$x = - \frac{12}{11} - \frac{8 i}{11} \sqrt{6} , x = \frac{230}{11} + \frac{8 i}{11} \sqrt{6}$

$x = \frac{21}{11} - \frac{8 i}{11} \sqrt{6} , x = - \frac{1}{11} + \frac{8 i}{11} \sqrt{6}$

$x = \frac{20}{11} - \frac{16 i}{11} \sqrt{6} , x = - \frac{20}{11} - \frac{16 i}{11} \sqrt{6}$

$x = \frac{10}{11} - \frac{8 i}{11} \sqrt{6} , x = \frac{10}{11} + \frac{8 i}{11} \sqrt{6}$

Correct answer:

$x = \frac{10}{11} - \frac{8 i}{11} \sqrt{6} , x = \frac{10}{11} + \frac{8 i}{11} \sqrt{6}$

Explanation:

We can solve this by using the quadratic formula.

The quadratic formula is

$\frac{ -b \pm\sqrt{ b^{2} - 4 a c}}{2a}$

$\uptext{a}$ , $\uptext{b}$ , and $\uptext{c}$ correspond to coefficients in the quadratic equation, which is

$a x^{2} + b x - 44 = 0$

In this case a = -11 , b = 20 , and c = -44 .

$\frac{ -20 \pm\sqrt{ 20 ^2- 4 \cdot -11 \cdot -44 }}{ 2 \cdot -11 }$

$\frac{ -20 \pm\sqrt{ 400 - 1936 }}{ -22 }$

$\frac{ -20 \pm\sqrt{ -1536 }}{ -22 }$

Since the number inside the square root is negative, we will have an imaginary answer.

We will put an $\uptext{i}$ , outside the square root sign, and then do normal operations.

$\frac{ -20 \pm i \sqrt{ 1536 }}{ -22 }$

Now we split this up into two equations.

$\frac{ -20 + i \sqrt{ 1536 }}{ -22 }$

$\frac{10}{11} + \frac{8 i}{11} \sqrt{6}$

$\frac{ -20 - i \sqrt{ 1536 }}{ -22 }$

$\frac{10}{11} - \frac{8 i}{11} \sqrt{6}$

So our solutions are $x = \frac{10}{11} - \frac{8 i}{11} \sqrt{6}$ and $x = \frac{10}{11} + \frac{8 i}{11} \sqrt{6}$

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Example Question #2 : Solve Quadratic Equations By Inspection, Quadratic Formula, Factoring, Completing The Square, And Taking Square Roots: Ccss.Math.Content.Hsa Rei.B.4b

Solve $18 x^{2} - 14 x + 41 = 0$

Possible Answers:

$x = \frac{7}{18} - \frac{\sqrt{689} i}{18} , x = \frac{7}{18} + \frac{\sqrt{689} i}{18}$

$x = - \frac{29}{18} - \frac{\sqrt{689} i}{18} , x = \frac{367}{18} + \frac{\sqrt{689} i}{18}$

$x = \frac{25}{18} - \frac{\sqrt{689} i}{18} , x = - \frac{11}{18} + \frac{\sqrt{689} i}{18}$

$x = \frac{7}{9} - \frac{\sqrt{689} i}{9} , x = - \frac{7}{9} - \frac{\sqrt{689} i}{9}$

$x = \frac{187}{18} - \frac{\sqrt{689} i}{18} , x = - \frac{173}{18} + \frac{\sqrt{689} i}{18}$

Correct answer:

$x = \frac{7}{18} - \frac{\sqrt{689} i}{18} , x = \frac{7}{18} + \frac{\sqrt{689} i}{18}$

Explanation:

We can solve this by using the quadratic formula.

The quadratic formula is

$\frac{ -b \pm\sqrt{ b^{2} - 4 a c }}{ 2 a }$

$\uptext{a}$ , $\uptext{b}$ , and $\uptext{c}$ correspond to coefficients in the quadratic equation, which is

$a x^{2} + b x + 41 = 0$

In this case a = 18 , b = -14 , and c = 41 .

$\frac{ 14 \pm\sqrt{ -14 ^2- 4 \cdot 18 \cdot 41 }}{ 2 \cdot 18 }$

$\frac{ 14 \pm\sqrt{ 196 - 2952 }}{ 36 }$

$\frac{ 14 \pm\sqrt{ -2756 }}{ 36 }$

Since the number inside the square root is negative, we will have an imaginary answer.

We will put an $\uptext{i}$ , outside the square root sign, and then do normal operations.

$\frac{ 14 \pm i \sqrt{ 2756 }}{ 36 }$

Now we split this up into two equations.

$\frac{ 14 + i \sqrt{ 2756 }}{ 36 }$

$\frac{7}{18} + \frac{\sqrt{689} i}{18}$

$\frac{ 14 - i \sqrt{ 2756 }}{ 36 }$

$\frac{7}{18} - \frac{\sqrt{689} i}{18}$

So our solutions are $x = \frac{7}{18} - \frac{\sqrt{689} i}{18}$ and $x = \frac{7}{18} + \frac{\sqrt{689} i}{18}$

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Example Question #3 : Solve Quadratic Equations By Inspection, Quadratic Formula, Factoring, Completing The Square, And Taking Square Roots: Ccss.Math.Content.Hsa Rei.B.4b

Solve $22 x^{2} - 9 x + 16 = 0$

Possible Answers:

$x = \frac{53}{44} - \frac{\sqrt{1327} i}{44} , x = - \frac{35}{44} + \frac{\sqrt{1327} i}{44}$

$x = \frac{9}{44} - \frac{\sqrt{1327} i}{44} , x = \frac{9}{44} + \frac{\sqrt{1327} i}{44}$

$x = - \frac{79}{44} - \frac{\sqrt{1327} i}{44} , x = \frac{889}{44} + \frac{\sqrt{1327} i}{44}$

$x = \frac{449}{44} - \frac{\sqrt{1327} i}{44} , x = - \frac{431}{44} + \frac{\sqrt{1327} i}{44}$

$x = \frac{9}{22} - \frac{\sqrt{1327} i}{22} , x = - \frac{9}{22} - \frac{\sqrt{1327} i}{22}$

Correct answer:

$x = \frac{9}{44} - \frac{\sqrt{1327} i}{44} , x = \frac{9}{44} + \frac{\sqrt{1327} i}{44}$

Explanation:

We can solve this by using the quadratic formula.

The quadratic formula is

$\frac{ -b \pm\sqrt{ b^{2} - 4 a c }}{ 2 a }$

$\uptext{a}$ , $\uptext{b}$ , and $\uptext{c}$ correspond to coefficients in the quadratic equation, which is

$a x^{2} + b x + 16 = 0$

In this case a = 22 , b = -9 , and c = 16 .

$\frac{ 9 \pm\sqrt{ -9 ^2- 4 \cdot 22 \cdot 16 }}{ 2 \cdot 22 }$

$\frac{ 9 \pm\sqrt{ 81 - 1408 }}{ 44 }$

$\frac{ 9 \pm\sqrt{ -1327 }}{ 44 }$

Since the number inside the square root is negative, we will have an imaginary answer.

We will put an $\uptext{i}$ , outside the square root sign, and then do normal operations.

$\frac{ 9 \pm i \sqrt{ 1327 }}{ 44 }$

Now we split this up into two equations.

$\frac{ 9 + i \sqrt{ 1327 }}{ 44 }$

$\frac{9}{44} + \frac{\sqrt{1327} i}{44}$

$\frac{ 9 - i \sqrt{ 1327 }}{ 44 }$

$\frac{9}{44} - \frac{\sqrt{1327} i}{44}$

So our solutions are $x = \frac{9}{44} - \frac{\sqrt{1327} i}{44}$ and $x = \frac{9}{44} + \frac{\sqrt{1327} i}{44}$

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Example Question #4 : Solve Quadratic Equations By Inspection, Quadratic Formula, Factoring, Completing The Square, And Taking Square Roots: Ccss.Math.Content.Hsa Rei.B.4b

Solve $- 49 x^{2} + 17 x - 45 = 0$

Possible Answers:

$x = \frac{115}{98} - \frac{\sqrt{8531} i}{98} , x = - \frac{81}{98} + \frac{\sqrt{8531} i}{98}$

$x = \frac{17}{49} - \frac{\sqrt{8531} i}{49} , x = - \frac{17}{49} - \frac{\sqrt{8531} i}{49}$

$x = - \frac{179}{98} - \frac{\sqrt{8531} i}{98} , x = \frac{1977}{98} + \frac{\sqrt{8531} i}{98}$

$x = \frac{17}{98} - \frac{\sqrt{8531} i}{98} , x = \frac{17}{98} + \frac{\sqrt{8531} i}{98}$

$x = \frac{997}{98} - \frac{\sqrt{8531} i}{98} , x = - \frac{963}{98} + \frac{\sqrt{8531} i}{98}$

Correct answer:

$x = \frac{17}{98} - \frac{\sqrt{8531} i}{98} , x = \frac{17}{98} + \frac{\sqrt{8531} i}{98}$

Explanation:

We can solve this by using the quadratic formula.

The quadratic formula is

$\frac{ -b \pm\sqrt{ b^{2} - 4 a c }}{ 2 a }$

$\uptext{a}$ , $\uptext{b}$ , and $\uptext{c}$ correspond to coefficients in the quadratic equation, which is

$a x^{2} + b x - 45 = 0$

In this case a = -49 , b = 17 , and c = -45 .

$\frac{ -17 \pm\sqrt{ 17 ^2- 4 \cdot -49 \cdot -45 }}{ 2 \cdot -49 }$

$\frac{ -17 \pm\sqrt{ 289 - 8820 }}{ -98 }$

$\frac{ -17 \pm\sqrt{ -8531 }}{ -98 }$

Since the number inside the square root is negative, we will have an imaginary answer.

We will put an $\uptext{i}$ , outside the square root sign, and then do normal operations.

$\frac{ -17 \pm i \sqrt{ 8531 }}{ -98 }$

Now we split this up into two equations.

$\frac{ -17 + i \sqrt{ 8531 }}{ -98 }$

$\frac{17}{98} + \frac{\sqrt{8531} i}{98}$

$\frac{ -17 - i \sqrt{ 8531 }}{ -98 }$

$\frac{17}{98} - \frac{\sqrt{8531} i}{98}$

So our solutions are $x = \frac{17}{98} - \frac{\sqrt{8531} i}{98}$ and $x = \frac{17}{98} + \frac{\sqrt{8531} i}{98}$

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Example Question #5 : Solve Quadratic Equations By Inspection, Quadratic Formula, Factoring, Completing The Square, And Taking Square Roots: Ccss.Math.Content.Hsa Rei.B.4b

Solve $28 x^{2} + 30 x + 32 = 0$

Possible Answers:

$x = \frac{13}{28} - \frac{\sqrt{671} i}{28} , x = - \frac{43}{28} + \frac{\sqrt{671} i}{28}$

$x = - \frac{15}{14} - \frac{\sqrt{671} i}{14} , x = \frac{15}{14} - \frac{\sqrt{671} i}{14}$

$x = - \frac{71}{28} - \frac{\sqrt{671} i}{28} , x = \frac{545}{28} + \frac{\sqrt{671} i}{28}$

$x = - \frac{15}{28} - \frac{\sqrt{671} i}{28} , x = - \frac{15}{28} + \frac{\sqrt{671} i}{28}$

$x = \frac{265}{28} - \frac{\sqrt{671} i}{28} , x = - \frac{295}{28} + \frac{\sqrt{671} i}{28}$

Correct answer:

$x = - \frac{15}{28} - \frac{\sqrt{671} i}{28} , x = - \frac{15}{28} + \frac{\sqrt{671} i}{28}$

Explanation:

We can solve this by using the quadratic formula.

The quadratic formula is

$\frac{ -b \pm\sqrt{ b^{2} - 4 a c }}{ 2 a }$

$\uptext{a}$ , $\uptext{b}$ , and $\uptext{c}$ correspond to coefficients in the quadratic equation, which is

$a x^{2} + b x + 32 = 0$

In this case a = 28 , b = 30 , and c = 32 .

$\frac{ -30 \pm\sqrt{ 30 ^2- 4 \cdot 28 \cdot 32 }}{ 2 \cdot 28 }$

$\frac{ -30 \pm\sqrt{ 900 - 3584 }}{ 56 }$

$\frac{ -30 \pm\sqrt{ -2684 }}{ 56 }$

Since the number inside the square root is negative, we will have an imaginary answer.

We will put an $\uptext{i}$ , outside the square root sign, and then do normal operations.

$\frac{ -30 \pm i \sqrt{ 2684 }}{ 56 }$

Now we split this up into two equations.

$\frac{ -30 + i \sqrt{ 2684 }}{ 56 }$

$- \frac{15}{28} + \frac{\sqrt{671} i}{28}$

$\frac{ -30 - i \sqrt{ 2684 }}{ 56 }$

$- \frac{15}{28} - \frac{\sqrt{671} i}{28}$

So our solutions are $x = - \frac{15}{28} - \frac{\sqrt{671} i}{28}$ and $x = - \frac{15}{28} + \frac{\sqrt{671} i}{28}$

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Example Question #6 : Solve Quadratic Equations By Inspection, Quadratic Formula, Factoring, Completing The Square, And Taking Square Roots: Ccss.Math.Content.Hsa Rei.B.4b

Solve $- 49 x^{2} + 24 x - 40 = 0$

Possible Answers:

$x = - \frac{86}{49} - \frac{2 i}{49} \sqrt{454} , x = \frac{992}{49} + \frac{2 i}{49} \sqrt{454}$

$x = \frac{61}{49} - \frac{2 i}{49} \sqrt{454} , x = - \frac{37}{49} + \frac{2 i}{49} \sqrt{454}$

$x = \frac{24}{49} - \frac{4 i}{49} \sqrt{454} , x = - \frac{24}{49} - \frac{4 i}{49} \sqrt{454}$

$x = \frac{502}{49} - \frac{2 i}{49} \sqrt{454} , x = - \frac{478}{49} + \frac{2 i}{49} \sqrt{454}$

$x = \frac{12}{49} - \frac{2 i}{49} \sqrt{454} , x = \frac{12}{49} + \frac{2 i}{49} \sqrt{454}$

Correct answer:

$x = \frac{12}{49} - \frac{2 i}{49} \sqrt{454} , x = \frac{12}{49} + \frac{2 i}{49} \sqrt{454}$

Explanation:

We can solve this by using the quadratic formula.

The quadratic formula is

$\frac{ -b \pm\sqrt{ b^{2} - 4 a c }}{ 2 a }$

$\uptext{a}$ , $\uptext{b}$ , and $\uptext{c}$ correspond to coefficients in the quadratic equation, which is

$a x^{2} + b x - 40 = 0$

In this case a = -49 , b = 24 , and c = -40 .

$\frac{ -24 \pm\sqrt{ 24 ^2- 4 \cdot -49 \cdot -40 }}{ 2 \cdot -49 }$

$\frac{ -24 \pm\sqrt{ 576 - 7840 }}{ -98 }$

$\frac{ -24 \pm\sqrt{ -7264 }}{ -98 }$

Since the number inside the square root is negative, we will have an imaginary answer.

We will put an $\uptext{i$ , outside the square root sign, and then do normal operations.

$\frac{ -24 \pm i \sqrt{ 7264 }}{ -98 }$

Now we split this up into two equations.

$\frac{ -24 + i \sqrt{ 7264 }}{ -98 }$

$\frac{12}{49} + \frac{2 i}{49} \sqrt{454}$

$\frac{ -24 - i \sqrt{ 7264 }}{ -98 }$

$\frac{12}{49} - \frac{2 i}{49} \sqrt{454}$

So our solutions are $x = \frac{12}{49} - \frac{2 i}{49} \sqrt{454}$ and $x = \frac{12}{49} + \frac{2 i}{49} \sqrt{454}$

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Example Question #1 : Solve Quadratic Equations By Inspection, Quadratic Formula, Factoring, Completing The Square, And Taking Square Roots: Ccss.Math.Content.Hsa Rei.B.4b

Solve $- 41 x^{2} + 46 x - 20 = 0$

Possible Answers:

$x = - \frac{59}{41} - \frac{\sqrt{291} i}{41} , x = \frac{843}{41} + \frac{\sqrt{291} i}{41}$

$x = \frac{64}{41} - \frac{\sqrt{291} i}{41} , x = - \frac{18}{41} + \frac{\sqrt{291} i}{41}$

$x = \frac{23}{41} - \frac{\sqrt{291} i}{41} , x = \frac{23}{41} + \frac{\sqrt{291} i}{41}$

$x = \frac{46}{41} - \frac{2 i}{41} \sqrt{291} , x = - \frac{46}{41} - \frac{2 i}{41} \sqrt{291}$

$x = \frac{433}{41} - \frac{\sqrt{291} i}{41} , x = - \frac{387}{41} + \frac{\sqrt{291} i}{41}$

Correct answer:

$x = \frac{23}{41} - \frac{\sqrt{291} i}{41} , x = \frac{23}{41} + \frac{\sqrt{291} i}{41}$

Explanation:

We can solve this by using the quadratic formula.

The quadratic formula is

$\frac{ -b \pm\sqrt{ b^{2} - 4 a c }}{ 2 a }$

$\uptext{a}$ , $\uptext{b}$ , and $\uptext{c}$ correspond to coefficients in the quadratic equation, which is

$a x^{2} + b x - 20 = 0$

In this case a = -41 , b = 46 , and c = -20 .

$\frac{ -46 \pm\sqrt{ 46 ^2- 4 \cdot -41 \cdot -20 }}{ 2 \cdot -41 }$

$\frac{ -46 \pm\sqrt{ 2116 - 3280 }}{ -82 }$

$\frac{ -46 \pm\sqrt{ -1164 }}{ -82 }$

Since the number inside the square root is negative, we will have an imaginary answer.

We will put an \uptext{i}, outside the square root sign, and then do normal operations.

$\frac{ -46 \pm i \sqrt{ 1164 }}{ -82 }$

Now we split this up into two equations.

$\frac{ -46 + i \sqrt{ 1164 }}{ -82 }$

$\frac{23}{41} + \frac{\sqrt{291} i}{41}$

$\frac{ -46 - i \sqrt{ 1164 }}{ -82 }$

$\frac{23}{41} - \frac{\sqrt{291} i}{41}$

So our solutions are $x = \frac{23}{41} - \frac{\sqrt{291} i}{41}$ and $x = \frac{23}{41} + \frac{\sqrt{291} i}{41}$

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Example Question #8 : Solve Quadratic Equations By Inspection, Quadratic Formula, Factoring, Completing The Square, And Taking Square Roots: Ccss.Math.Content.Hsa Rei.B.4b

Solve $- 12 x^{2} - 27 x - 30 = 0$

Possible Answers:

$x = \frac{71}{8} - \frac{\sqrt{79} i}{8} , x = - \frac{89}{8} + \frac{\sqrt{79} i}{8}$

$x = - \frac{25}{8} - \frac{\sqrt{79} i}{8} , x = \frac{151}{8} + \frac{\sqrt{79} i}{8}$

$x = - \frac{9}{8} - \frac{\sqrt{79} i}{8} , x = - \frac{9}{8} + \frac{\sqrt{79} i}{8}$

$x = - \frac{1}{8} - \frac{\sqrt{79} i}{8} , x = - \frac{17}{8} + \frac{\sqrt{79} i}{8}$

$x = - \frac{9}{4} - \frac{\sqrt{79} i}{4} , x = \frac{9}{4} - \frac{\sqrt{79} i}{4}$

Correct answer:

$x = - \frac{9}{8} - \frac{\sqrt{79} i}{8} , x = - \frac{9}{8} + \frac{\sqrt{79} i}{8}$

Explanation:

We can solve this by using the quadratic formula.

The quadratic formula is

$\frac{ -b \pm\sqrt{ b^{2} - 4 a c }}{ 2 a }$

$\uptext{a}$ , $\uptext{b}$ , and $\uptext{c}$ correspond to coefficients in the quadratic equation, which is

$a x^{2} + b x - 30 = 0$

In this case a = -12 , b = -27 , and c = -30 .

$\frac{ 27 \pm\sqrt{ -27 ^2- 4 \cdot -12 \cdot -30 }}{ 2 \cdot -12 }$

$\frac{ 27 \pm\sqrt{ 729 - 1440 }}{ -24 }$

$\frac{ 27 \pm\sqrt{ -711 }}{ -24 }$

Since the number inside the square root is negative, we will have an imaginary answer.

We will put an $\uptext{i}$ , outside the square root sign, and then do normal operations.

$\frac{ 27 \pm i \sqrt{ 711 }}{ -24 }$

Now we split this up into two equations.

$\frac{ 27 + i \sqrt{ 711 }}{ -24 }$

$- \frac{9}{8} + \frac{\sqrt{79} i}{8}$

$\frac{ 27 - i \sqrt{ 711 }}{ -24 }$

$- \frac{9}{8} - \frac{\sqrt{79} i}{8}$

So our solutions are $x = - \frac{9}{8} - \frac{\sqrt{79} i}{8}$ and $x = - \frac{9}{8} + \frac{\sqrt{79} i}{8}$

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Example Question #9 : Solve Quadratic Equations By Inspection, Quadratic Formula, Factoring, Completing The Square, And Taking Square Roots: Ccss.Math.Content.Hsa Rei.B.4b

Solve $- 23 x^{2} + 34 x - 44 = 0$

Possible Answers:

$x = \frac{34}{23} - \frac{2 i}{23} \sqrt{723} , x = - \frac{34}{23} - \frac{2 i}{23} \sqrt{723}$

$x = \frac{17}{23} - \frac{\sqrt{723} i}{23} , x = \frac{17}{23} + \frac{\sqrt{723} i}{23}$

$x = \frac{247}{23} - \frac{\sqrt{723} i}{23} , x = - \frac{213}{23} + \frac{\sqrt{723} i}{23}$

$x = \frac{40}{23} - \frac{\sqrt{723} i}{23} , x = - \frac{6}{23} + \frac{\sqrt{723} i}{23}$

$x = - \frac{29}{23} - \frac{\sqrt{723} i}{23} , x = \frac{477}{23} + \frac{\sqrt{723} i}{23}$

Correct answer:

$x = \frac{17}{23} - \frac{\sqrt{723} i}{23} , x = \frac{17}{23} + \frac{\sqrt{723} i}{23}$

Explanation:

We can solve this by using the quadratic formula.

The quadratic formula is

$\frac{ -b \pm\sqrt{ b^{2} - 4 a c }}{ 2 a }$

$\uptext{a}$ , $\uptext{b}$ , and $\uptext{c}$ correspond to coefficients in the quadratic equation, which is

$a x^{2} + b x - 44 = 0$

In this case a = -23 , b = 34 , and c = -44 .

$\frac{ -34 \pm\sqrt{ 34 ^2- 4 \cdot -23 \cdot -44 }}{ 2 \cdot -23 }$

$\frac{ -34 \pm\sqrt{ 1156 - 4048 }}{ -46 }$

$\frac{ -34 \pm\sqrt{ -2892 }}{ -46 }$

Since the number inside the square root is negative, we will have an imaginary answer.

We will put an $\uptext{i}$ , outside the square root sign, and then do normal operations.

$\frac{ -34 \pm i \sqrt{ 2892 }}{ -46 }$

Now we split this up into two equations.

$\frac{ -34 + i \sqrt{ 2892 }}{ -46 }$

$\frac{17}{23} + \frac{\sqrt{723} i}{23}$

$\frac{ -34 - i \sqrt{ 2892 }}{ -46 }$

$\frac{17}{23} - \frac{\sqrt{723} i}{23}$

So our solutions are $x = \frac{17}{23} - \frac{\sqrt{723} i}{23}$ and $x = \frac{17}{23} + \frac{\sqrt{723} i}{23}$

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Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

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Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

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Common Core: High School - Algebra : Reasoning with Equations & Inequalities

Study concepts, example questions & explanations for Common Core: High School - Algebra

All Common Core: High School - Algebra Resources

Example Questions

Example Question #51 : Reasoning With Equations & Inequalities

$x^{2} + 19 x - 52 = 0$

Example Question #1 : Solve Quadratic Equations By Inspection, Quadratic Formula, Factoring, Completing The Square, And Taking Square Roots: Ccss.Math.Content.Hsa Rei.B.4b

Example Question #2 : Solve Quadratic Equations By Inspection, Quadratic Formula, Factoring, Completing The Square, And Taking Square Roots: Ccss.Math.Content.Hsa Rei.B.4b

Example Question #3 : Solve Quadratic Equations By Inspection, Quadratic Formula, Factoring, Completing The Square, And Taking Square Roots: Ccss.Math.Content.Hsa Rei.B.4b

Example Question #4 : Solve Quadratic Equations By Inspection, Quadratic Formula, Factoring, Completing The Square, And Taking Square Roots: Ccss.Math.Content.Hsa Rei.B.4b

Example Question #5 : Solve Quadratic Equations By Inspection, Quadratic Formula, Factoring, Completing The Square, And Taking Square Roots: Ccss.Math.Content.Hsa Rei.B.4b

Example Question #6 : Solve Quadratic Equations By Inspection, Quadratic Formula, Factoring, Completing The Square, And Taking Square Roots: Ccss.Math.Content.Hsa Rei.B.4b

Example Question #1 : Solve Quadratic Equations By Inspection, Quadratic Formula, Factoring, Completing The Square, And Taking Square Roots: Ccss.Math.Content.Hsa Rei.B.4b

Example Question #8 : Solve Quadratic Equations By Inspection, Quadratic Formula, Factoring, Completing The Square, And Taking Square Roots: Ccss.Math.Content.Hsa Rei.B.4b

Example Question #9 : Solve Quadratic Equations By Inspection, Quadratic Formula, Factoring, Completing The Square, And Taking Square Roots: Ccss.Math.Content.Hsa Rei.B.4b

All Common Core: High School - Algebra Resources

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