Chapter 10: Q 87 (page 1181)

Solve the equation by completing square method.
$(x + 6) (x - 2) = 9$

Short Answer

Expert verified

The solutions are $x = - 7, x = 3$ .

Step by step solution

Given Information

The Given equation is $(x + 6) (x - 2) = 9$ .

Multiply the binomials on left.

$x^{2} + 4 x - 12 = 9$

Isolate the variables.

$x^{2} + 4 x = 9 + 12$

$x^{2} + 4 x = 21$

Here, $b = 4$ .

So,

$= {(\frac{b}{2})}^{2} = {(\frac{4}{2})}^{2} = {(2)}^{2} = 4$

Add $4$ both sides.

$x^{2} + 4 x + 4 = 21 + 4 x^{2} + 4 x + 4 = 25$

Factor the perfect square trinomial as a binomial square.

$(x + 2)^{2} = 25$

Use the square root property.

$x + 2 = \pm \sqrt{25} x + 2 = \pm 5 x = - 2 \pm 5$

Rewrite to show two solutions.

$x = - 2 + 5 = 3 x = - 2 - 5 = - 7$

Therefore, $x = - 7, x = 3$

Check the solutions.

Substitute $x = - 7$

$(x + 6) (x - 2) = 9 (- 7 + 6) (- 7 - 2) \overset{?}{=} 9 (- 1) (- 9) \overset{?}{=} 9 9 = 9 T r u e$

Substitute $x = 3$

$(x + 6) (x - 2) = 9 (3 + 6) (3 - 2) \overset{?}{=} 9 (9) (1) \overset{?}{=} 9 9 = 9 T r u e$

Thus, the solutions are $x = - 7, x = 3$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Solve the equation by completing square method.
$(x + 6) (x - 2) = 9$

Short Answer

Step by step solution

Given Information

Multiply the binomials on left.

Factor the perfect square trinomial as a binomial square.

Check the solutions.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

Applied Mathematics

Logic and Functions

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve the equation by completing square method. (x+6)(x-2)=9

Short Answer

Step by step solution

Given Information

Multiply the binomials on left.

Factor the perfect square trinomial as a binomial square.

Check the solutions.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

Applied Mathematics

Logic and Functions

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve the equation by completing square method.
$(x + 6) (x - 2) = 9$