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Common Core: High School - Algebra : Use Completing the Square to Derive the Quadratic Formula: CCSS.Math.Content.HSA-REI.B.4a

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

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All Common Core: High School - Algebra Resources

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Example Questions

Example Question #507 : High School: Algebra

Solve $x^{2} + 19 x - 34 = 0$ by completing the square. Round your answer to the nearest hundredth.

Possible Answers:

x = 1.65 , x = -20.65

x = -8.53, x = 0.05

x = -0.85, x = -18.15

x = -33.8, x = -13.2

x = 1.15, x = -20.15

Correct answer:

x = 1.65 , x = -20.65

Explanation:

The first step is to add to both sides.

$x^{2} + 19 x - 34 + 34 = 0 + 34$

$x^{2} + 19 x = 34$

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

$x^{2} + 19 x + \frac{19}{2} ^2 = 34 + \frac{19}{2} ^2$

$x^{2} + 19 x + \frac{361}{4} = 34 + \frac{361}{4}$

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

$\left( x + \frac{19}{2} \right)^2= \frac{497}{4}$

Now we take the square root of each side.

$\sqrt{\left( x + \frac{19}{2} \right)^2}= \sqrt{ \frac{497}{4} }$

$x + \frac{19}{2} = \sqrt{ \frac{497}{4} }$

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

$x + \frac{19}{2} - \frac{19}{2} = \sqrt{ \frac{497}{4} }- \frac{19}{2}$

$x = - \frac{19}{2} + \frac{\sqrt{497}}{2}$

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

$x = - \frac{19}{2} + \frac{\sqrt{497}}{2}$

x = 1.65

$x = - \frac{\sqrt{497}}{2} - \frac{19}{2}$

x = -20.65

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Example Question #501 : High School: Algebra

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

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

Possible Answers:

x = 1.93, x = -20.93

x = -3.38, x = 7.28

x = -5.2, x = -7.4

x = 2.43 , x = -21.43

x = -0.06, x = -18.93

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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All Common Core: High School - Algebra Resources

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Common Core: High School - Algebra : Use Completing the Square to Derive the Quadratic Formula: CCSS.Math.Content.HSA-REI.B.4a

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

All Common Core: High School - Algebra Resources

Example Questions

Example Question #507 : High School: Algebra

Example Question #501 : High School: Algebra

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

All Common Core: High School - Algebra Resources

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