Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Quadratic Equations and Inequalities

Study concepts, example questions & explanations for Algebra II

Create An Account

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #271 : Quadratic Equations And Inequalities

What will be the equation after completing the square? x^2-4x = -7

Possible Answers:

(x-2)^2= -4

(x-2)^2= -3

(x+2)^2= -3

(x-2)^2= -10

(x+2)^2=- 4

Correct answer:

(x-2)^2= -3

Explanation:

To complete the square, we will need to divide the coefficient of the x-variable on the left side of the equation.

$-4x \rightarrow\frac{-4}{2} = 2$

Square this number, and add it on both sides of the equation.

x^2-4x+4 = -7+4

Notice that the left side of the equation can be factorized by a single binomial squared. Simplify the right side as well.

The answer is: (x-2)^2= -3

Report an Error

Example Question #46 : Completing The Square

Solve by completing the square:

x^2-6x+2=0

Possible Answers:

$x=4.12\text{ or }0.33$

$x=9.12\text{ or }0.13$

$x=5.65\text{ or }0.35$

$x=3.29 \text{ or }1.31$

Correct answer:

$x=5.65\text{ or }0.35$

Explanation:

Start by moving the number to the right of the equation so that all the terms with values are alone:

x^2-6x+2=0

x^2-6x=-2

Now, you need to figure out what number to add to both sides. To do so, take the coefficient in front of the term, divide it by , then square it:

Coefficient:

$\text{Term to add}=(\frac{-6}{2})^2=(-3)^2=9$

Add this number to both sides of the equation:

x^2-6x+9=-2+9=7

Simplify the left side of the equation.

(x-3)^2=7

Now solve for .

$x-3=\pm\sqrt7$

$x=3+\sqrt7 = 5.65$ , or

$x=3-\sqrt7=0.35$

Make sure to round to places after the decimal.

Report an Error

Example Question #47 : Completing The Square

Solve the following quadratic equation by completing the square:

x^2+14x-20=0

Possible Answers:

$x=0.19\text{ or }-13.22$

$x=3.65\text{ or }-10.01$

$x=5.61\text{ or }-14.19$

$x=1.17\text{ or }-20.51$

$x=1.31\text{ or }-15.31$

Correct answer:

$x=1.31\text{ or }-15.31$

Explanation:

Start by moving the number to the right of the equation so that all the terms with values are alone:

x^2+14x-20=0

x^2+14x=20

Now, you need to figure out what number to add to both sides. To do so, take the coefficient in front of the term, divide it by , then square it:

Coefficient:

$\text{Term to add}=(\frac{14}{2})^2=(7)^2=49$

Add this number to both sides of the equation:

x^2+14x+49=20+49=69

Simplify the left side of the equation.

(x+7)^2=69

Now solve for .

$x+7=\pm\sqrt{69}$

$x=-7+\sqrt{69}=1.31$ , or

$x=-7-\sqrt{69}=-15.31$

Make sure to round to places after the decimal.

Report an Error

Example Question #48 : Completing The Square

Solve the following quadratic equation by completing the square:

x^2+12x-1=0

Possible Answers:

$x=1.19\text{ or }-10.68$

$x=0.12\text{ or }-14.12$

$x=0.09\text{ or }-19.47$

$x=0.08\text{ or }-12.08$

Correct answer:

$x=0.08\text{ or }-12.08$

Explanation:

Start by moving the number to the right of the equation so that all the terms with values are alone:

x^2+12x-1=0

x^2+12x=1

Now, you need to figure out what number to add to both sides. To do so, take the coefficient in front of the term, divide it by , then square it:

Coefficient:

$\text{Term to add}=(\frac{12}{2})^2=(6)^2=36$

Add this number to both sides of the equation:

x^2+12x+36=1+36=37

Simplify the left side of the equation.

(x+6)^2=37

Now solve for .

$x+6=\pm\sqrt{37}$

$x=-6+\sqrt{37}=0.08$ , or

$x=-6-\sqrt{37}=-12.08$

Make sure to round to places after the decimal.

Report an Error

Example Question #49 : Completing The Square

Solve the following quadratic equation by completing the square:

2x^2+6x-9=0

Possible Answers:

$x=1.10\text{ or }-4.10$

$x=2.28\text{ or }-1.61$

$x=2.14\text{ or }-10.40$

$x=4.29\text{ or }-2.11$

Correct answer:

$x=1.10\text{ or }-4.10$

Explanation:

Start by dividing the entire equation by the coefficient in front of x^2 , which is .

2x^2+6x-9=0

$x^2+3x-\frac{9}{2}=0$

Then, move the number to the right of the equation so that all the terms with values are alone:

$x^2+3x=\frac{9}{2}$

Now, you need to figure out what number to add to both sides. To do so, take the coefficient in front of the term, divide it by , then square it:

Coefficient:

$\text{Term to add}=(\frac{3}{2})^2=\frac{9}{4}$

Add this number to both sides of the equation:

$x^2+3x+\frac{9}{4}=\frac{9}{2}+\frac{9}{4}=\frac{27}{4}$

Simplify the left side of the equation.

$(x+\frac{3}{2})^2=\frac{27}{4}$

Now solve for .

$x+\frac{3}{2}=\pm\sqrt{\frac{27}{4}}$

$x=-\frac{3}{2}+\sqrt{\frac{27}{4}}=1.10$ , or

$x=-\frac{3}{2}-\sqrt{\frac{27}{4}}=-4.10$

Make sure to round to places after the decimal.

Report an Error

Example Question #50 : Completing The Square

Solve the quadratic equation by completing the square:

x^2-24x+100=0

Possible Answers:

$x=19.08\text{ or }4.11$

$x=17.76\text{ or }8.17$

$x=20.12\text{ or }12.55$

$x=18.63 \text{ or }5.37$

Correct answer:

$x=18.63 \text{ or }5.37$

Explanation:

Start by moving the number to the right of the equation so that all the terms with values are alone:

x^2-24x+100=0

x^2-24x=-100

Now, you need to figure out what number to add to both sides. To do so, take the coefficient in front of the term, divide it by , then square it:

Coefficient:

$\text{Term to add}=(\frac{-24}{2})^2=(-12)^2=144$

Add this number to both sides of the equation:

x^2-24x+144=-100+144=44

Simplify the left side of the equation.

(x-12)^2=44

Now solve for .

$x-12=\pm\sqrt{44}$

$x=12+\sqrt{44}=18.63$ , or

$x=12-\sqrt{44}=5.37$

Make sure to round to places after the decimal.

Report an Error

Example Question #51 : Completing The Square

Solve the following quadratic equation by completing the square:

x^2-10x+9=0

Possible Answers:

$x=4\text{ or }-9$

$x=-2\text{ or }2$

$x=1\text{ or } 9$

$x=-1\text{ or }-9$

Correct answer:

$x=1\text{ or } 9$

Explanation:

Start by moving the number to the right of the equation so that all the terms with values are alone:

x^2-10x+9=0

x^2-10x=-9

Now, you need to figure out what number to add to both sides. To do so, take the coefficient in front of the term, divide it by , then square it:

Coefficient:

$\text{Term to add}=(\frac{10}{2})^2=(5)^2=25$

Add this number to both sides of the equation:

x^2-10x+25=-9+25=16

Simplify the left side of the equation.

(x-5)^2=16

Now solve for .

$x-5=\pm4$

x=5+4=9 , or

x=5-4=1

Report an Error

Example Question #121 : Solving Quadratic Equations

Solve the quadratic equation by completing the square:

5x^2+20x-12=0

Possible Answers:

$x=0.53\text{ or }-4.53$

$x=1.01\text{ or }-2.15$

$x=0.09\text{ or }-1.66$

$x=0.71\text{ or }1.54$

Correct answer:

$x=0.53\text{ or }-4.53$

Explanation:

Start by dividing the entire equation by the coefficient in front of x^2 , which is .

5x^2+20x-12=0

$x^2+4x-\frac{12}{5}=0$

Then, move the number to the right of the equation so that all the terms with values are alone:

$x^2+4x=\frac{12}{5}$

Now, you need to figure out what number to add to both sides. To do so, take the coefficient in front of the term, divide it by , then square it:

Coefficient:

$\text{Term to add}=(\frac{4}{2})^2=2^2=4$

Add this number to both sides of the equation:

$x^2+4x+4=\frac{12}{5}+4=\frac{32}{5}$

Simplify the left side of the equation.

$(x+2)^2=\frac{32}{5}$

Now solve for .

$x+2=\pm\sqrt{\frac{32}{5}}$

$x=-2+\sqrt{\frac{32}{5}}=0.53$ , or

$x=-2-\sqrt{\frac{32}{5}}=-4.53$

Make sure to round to places after the decimal.

Report an Error

Example Question #122 : Solving Quadratic Equations

Solve the quadratic equation by completing the square:

x^2-18x+46=0

Possible Answers:

$x=20.59\text{ or }4.12$

$x=13.44\text{ or }6.24$

$x=14.92\text{ or }3.08$

$x=19.90\text{ or }0.18$

Correct answer:

$x=14.92\text{ or }3.08$

Explanation:

Start by moving the number to the right of the equation so that all the terms with values are alone:

x^2-18x+46=0

x^2-18x=-46

Now, you need to figure out what number to add to both sides. To do so, take the coefficient in front of the term, divide it by , then square it:

Coefficient:

$\text{Term to add}=(\frac{-18}{2})^2=(-9)^2=81$

Add this number to both sides of the equation:

x^2-18x+81=-46+81=35

Simplify the left side of the equation.

(x-9)^2=35

Now solve for .

$x-9=\pm\sqrt{35}$

$x=9+\sqrt{35}=14.92$ , or

$x=9-\sqrt{35}=3.08$

Make sure to round to places after the decimal.

Report an Error

Example Question #123 : Solving Quadratic Equations

Solve the quadratic equation by completing the square:

x^2+22x+100=0

Possible Answers:

$x=-9.01\text{ or }-18.23$

$x=-9.29\text{ or }-21.32$

$x=-5.45\text{ or }-15.61$

$x=-6.42\text{ or }-15.58$

Correct answer:

$x=-6.42\text{ or }-15.58$

Explanation:

Start by moving the number to the right of the equation so that all the terms with values are alone:

x^2+22x+100=0

x^2+22x=-100

Now, you need to figure out what number to add to both sides. To do so, take the coefficient in front of the term, divide it by , then square it:

Coefficient:

$\text{Term to add}=(\frac{22}{2})^2=(11)^2=121$

Add this number to both sides of the equation:

x^2+22x+121=-100+121=21

Simplify the left side of the equation.

(x+11)^2=21

Now solve for .

$x+11=\pm\sqrt{21}$

$x=-11+\sqrt{21}=-6.42$ , or

$x=-11-\sqrt{21}=-15.58$

Make sure to round to places after the decimal.

Report an Error

View Algebra 2 Tutors

Eashan
Certified Tutor

Rutgers University-New Brunswick, Bachelor of Science, Computer Science.

View Algebra 2 Tutors

Sharon
Certified Tutor

Tabor College, Bachelor of Science, Mathematics Teacher Education. Tabor College, Masters in Education, Education.

View Algebra 2 Tutors

Hayley
Certified Tutor

University of North Florida, Bachelor in Arts, English.

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Chemistry Tutors in Denver, ACT Tutors in Houston, SAT Tutors in Boston, Computer Science Tutors in Phoenix, Reading Tutors in Philadelphia, Computer Science Tutors in Los Angeles, Math Tutors in San Francisco-Bay Area, Chemistry Tutors in Dallas Fort Worth, ACT Tutors in Philadelphia, Physics Tutors in Seattle

Popular Courses & Classes

SAT Courses & Classes in Chicago, SAT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Atlanta, MCAT Courses & Classes in Chicago, ISEE Courses & Classes in Phoenix, SSAT Courses & Classes in Los Angeles, Spanish Courses & Classes in Washington DC

Popular Test Prep

MCAT Test Prep in Chicago, ACT Test Prep in Miami, ISEE Test Prep in Miami, GRE Test Prep in Atlanta, GRE Test Prep in Denver, ACT Test Prep in Atlanta, SSAT Test Prep in Phoenix, GMAT Test Prep in Miami, ISEE Test Prep in San Diego, GMAT Test Prep in Los Angeles

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

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

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

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.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Algebra II : Quadratic Equations and Inequalities

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #271 : Quadratic Equations And Inequalities

Example Question #46 : Completing The Square

Example Question #47 : Completing The Square

Example Question #48 : Completing The Square

Example Question #49 : Completing The Square

Example Question #50 : Completing The Square

Example Question #51 : Completing The Square

Example Question #121 : Solving Quadratic Equations

Example Question #122 : Solving Quadratic Equations

Example Question #123 : Solving Quadratic Equations

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: