10.2 Solve quadratic equations by completing the square (Page 2/5)

<< Chapter < Page

Elementary algebra Page 2 / 5

Chapter >> Page >

Complete the square to make a perfect square trinomial. Write the result as a binomial square.

$a^{2} - 20 a$

${(a - 10)}^{2}$

Got questions? Get instant answers now!

Complete the square to make a perfect square trinomial. Write the result as a binomial square.

$b^{2} - 4 b$

${(b - 2)}^{2}$

Got questions? Get instant answers now!

Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared.

$u^{2} - 9 u$

Solution

The coefficient of u is −9.
$\begin{matrix} Find {(\frac{1}{2} b)}^{2} . \\ {(\frac{1}{2} \cdot (− 9))}^{2} \\ {(- \frac{9}{2})}^{2} \\ \frac{81}{4} \end{matrix}$
Add $\frac{81}{4}$ to the binomial to complete the square.	$u^{2} - 9 u + \frac{81}{4}$
Rewrite as a binomial square.	${(u - \frac{9}{2})}^{2}$

Got questions? Get instant answers now!

Complete the square to make a perfect square trinomial. Write the result as a binomial square.

$m^{2} - 5 m$

${(m - \frac{5}{2})}^{2}$

Got questions? Get instant answers now!

Complete the square to make a perfect square trinomial. Write the result as a binomial square.

$n^{2} + 13 n$

${(n + \frac{13}{2})}^{2}$

Got questions? Get instant answers now!

Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared.

$p^{2} + \frac{1}{2} p$

Solution

The coefficient of p is $\frac{1}{2}$ .
$\begin{matrix} Find {(\frac{1}{2} b)}^{2} . \\ {(\frac{1}{2} \cdot \frac{1}{2})}^{2} \\ {(\frac{1}{4})}^{2} \\ \frac{1}{16} \end{matrix}$
Add $\frac{1}{16}$ to the binomial to complete the square.	$p^{2} + \frac{1}{2} p + \frac{1}{16}$
Rewrite as a binomial square.	${(p + \frac{1}{4})}^{2}$

Got questions? Get instant answers now!

Complete the square to make a perfect square trinomial. Write the result as a binomial square.

$p^{2} + \frac{1}{4} p$

${(p + \frac{1}{8})}^{2}$

Got questions? Get instant answers now!

Complete the square to make a perfect square trinomial. Write the result as a binomial square.

$q^{2} - \frac{2}{3} q$

${(q - \frac{1}{3})}^{2}$

Got questions? Get instant answers now!

Solve quadratic equations of the form x ² + bx + c = 0 by completing the square

In solving equations, we must always do the same thing to both sides of the equation. This is true, of course, when we solve a quadratic equation by completing the square , too. When we add a term to one side of the equation to make a perfect square trinomial, we must also add the same term to the other side of the equation.

For example, if we start with the equation $x^{2} + 6 x = 40$ and we want to complete the square on the left, we will add nine to both sides of the equation.

The image shows the equation x squared plus six x equals 40. Below that the equation is rewritten as x squared plus six x plus blank space equals 40 plus blank space. Below that the equation is rewritten again as x squared plus six x plus nine equals 40 plus nine.

Then, we factor on the left and simplify on the right.

{(x + 3)}^{2} = 49

Now the equation is in the form to solve using the Square Root Property. Completing the square is a way to transform an equation into the form we need to be able to use the Square Root Property.

How to solve a quadratic equation of the form $x^{2} + b x + c = 0$ By completing the square

Solve $x^{2} + 8 x = 48$ by completing the square.

Solution

The image shows the steps to solve the equation x squared plus eight x equals 48. Step one is to isolate the variable terms on one side and the constant terms on the other. The equation already has all the variables on the left.

Step two is to find the quantity half of b squared, the number to complete the square and add it to both sides of the equation. The coefficient of x is eight so b is eight. Take half of eight, which is four and square it to get 16. Add 16 to both sides of the equation to get x squared plus eight x plus 16 equals 48 plus 16.

Step three is to factor the perfect square trinomial as a binomial square. The left side is the perfect square trinomial x squared plus eight x plus 16 which factors to the quantity x plus four squared. Adding on the right side 48 plus 16 is 64. The equation is now the quantity x plus four squared equals 64.

Step four is to use the square root property to make the equation x plus four equals plus or minus the square root of 64.

Step five is to simplify the radical and then solve the two resulting equations. The square root of 64 is eight. The equation can be written as two equations: x plus four equals eight and x plus four equals negative eight. Solving each equation gives x equals four or negative 12.

Step six is to check the solutions. To check the solutions put each answer in the original equation. Substituting x equals four in the original equation to get four squared plus eight times four equals 48. The left side simplifies to 16 plus 32 which is 48. Substituting x equals negative 12 in the original equation to get negative 12 squared plus eight times negative 12 equals 48. The left side simplifies to 144 minus 96 which is 48.

Got questions? Get instant answers now!

Solve $c^{2} + 4 c = 5$ by completing the square.

$c = −5, c = 1$

Got questions? Get instant answers now!

Solve $d^{2} + 10 d = −9$ by completing the square.

$d = −9, d = −1$

Got questions? Get instant answers now!

Solve a quadratic equation of the form $x^{2} + b x + c = 0$ By completing the square.

Isolate the variable terms on one side and the constant terms on the other.
Find ${(\frac{1}{2} \cdot b)}^{2}$ , the number to complete the square. Add it to both sides of the equation.
Factor the perfect square trinomial as a binomial square.
Use the Square Root Property.
Simplify the radical and then solve the two resulting equations.
Check the solutions.

Solve $y^{2} - 6 y = 16$ by completing the square.

Solution

The variable terms are on the left side.
Take half of $- 6$ and square it. $(\frac{1}{2} (− 6))^{2} = 9$
Add 9 to both sides.
Factor the perfect square trinomial as a binomial square.
Use the Square Root Property.
Simplify the radical.
Solve for y .
Rewrite to show two solutions.
Solve the equations.
Check.

Got questions? Get instant answers now!

Solve $r^{2} - 4 r = 12$ by completing the square.

$r = −2, r = 6$

Got questions? Get instant answers now!

Solve $t^{2} - 10 t = 11$ by completing the square.

$t = −1, t = 11$

Got questions? Get instant answers now!

Questions & Answers

what does preconceived mean

sammie Reply

physiological Psychology

Nwosu Reply

How can I develope my cognitive domain

Amanyire Reply

why is communication effective

Dakolo Reply

Communication is effective because it allows individuals to share ideas, thoughts, and information with others.

effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.

it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.

miss

Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment

Wekolamo Reply

please i need answer

Wekolamo

because it helps many people around the world to understand how to interact with other people and understand them well, for example at work (job).

Manix Reply

Agreed 👍 There are many parts of our brains and behaviors, we really need to get to know. Blessings for everyone and happy Sunday!

ARC

A child is a member of community not society elucidate ?

JESSY Reply

Isn't practices worldwide, be it psychology, be it science. isn't much just a false belief of control over something the mind cannot truly comprehend?

Simon Reply

compare and contrast skinner's perspective on personality development on freud

namakula Reply

Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning

war

explain how nature and nurture affect the development and later the productivity of an individual.

Amesalu Reply

nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.

Samuel

I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills

Zyryn Reply

good👍

Jonathan

and having a good philosophy of the world is like a sandwich and a peanut butter 👍

Jonathan

generally amnesi how long yrs memory loss

Kelu Reply

interpersonal relationships

Abdulfatai Reply

What would be the best educational aid(s) for gifted kids/savants?

Heidi Reply

treat them normal, if they want help then give them. that will make everyone happy

Saurabh

What are the treatment for autism?

Magret Reply

hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities. before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these

Jharna

continue.. sometimes due to these physical problems..the diagnosis may be misdiagnosed. treatment for autism. well it depends on the severity. since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child

Jharna

child interact with other kids under doc supervision. play therapy. speech therapy. Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game. string and beads game. the more you interact with the child the more effective

Jharna

results you'll get.. please consult a therapist to know what suits best on your child. and last as a parent. I know sometimes it's overwhelming to guide a special kid. but trust the process and be strong and patient as a parent.

Jharna

Got questions? Join the online conversation and get instant answers!

Jobilize.com Reply

<< Chapter < Page Page > Chapter >>

Practice Key Terms 1

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

100% Free Mobile Applications
Receive real-time job alerts and never miss the right job again

Source: OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2

Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask

	45 Biology 45 Population and Community Ecology MCQ By OpenStax Start Quiz
	Understanding basic music theory By OpenStax Read Online Course
	11 AP Key Terms 11 The Muscular System By OpenStax Start Key Terms
©flickr: Donnie	How well do you know Beanie Boos? By Angela Eckman Start Quiz
	7 BOD Urinary Tract quiz By Brooke Delaney Start Exam
	3 Sociology 03 Culture MCQ By OpenStax Start Quiz
	NCE Ch 04 Social and Cultural Foundations By Anh Dao Start Quiz
	NCE Ch 06 Groups By Anh Dao Start Quiz
©flickr: Gage	How well do you know Ross Lynch? By Brianna Beck Start Quiz
	Microbiology Practice Test By Sandhills MLT Start Test

10.2 Solve quadratic equations by completing the square (Page 2/5)

Solution

Solution

Solve quadratic equations of the form x 2 + bx + c = 0 by completing the square

How to solve a quadratic equation of the form x 2 + b x + c = 0 By completing the square

Solution

Solve a quadratic equation of the form x 2 + b x + c = 0 By completing the square.

Solution

Questions & Answers

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Solve quadratic equations of the form x ² + bx + c = 0 by completing the square

How to solve a quadratic equation of the form $x^{2} + b x + c = 0$ By completing the square

Solve a quadratic equation of the form $x^{2} + b x + c = 0$ By completing the square.