Chapter 9: Q13. (page 597)

Solve each equation by completing the square.
$x^{2} - x - 6 = 0$

Short Answer

Expert verified

The solutions of the quadratic equation are $- 2$ and 3.

Step by step solution

Step 1. Complete the square

Complete the square to solve the quadratic equations by isolating $x^{2}$ andbx-terms.

$x^{2} - x - 6 = 0 x^{2} - x - 6 + \frac{1}{4} = 0 + \frac{1}{4} [Since {(\frac{1}{2})}^{2} = \frac{1}{4} add to each side] x^{2} - x + \frac{1}{4} - 6 + 6 = \frac{1}{4} + 6 [Add 6 to each side] x^{2} - x + \frac{1}{4} = \frac{25}{4}$

Step 2. Take the square root of each side

First factor $x^{2} - x + \frac{1}{4}$ , then take square root of each side.

${(x - \frac{1}{2})}^{2} = \frac{25}{4} \sqrt{{(x - \frac{1}{2})}^{2}} = \pm \sqrt{\frac{25}{4}} x - \frac{1}{2} = \pm \frac{5}{2}$

Step 3. Write the solutions

Add $\frac{1}{2}$ to both sides and separate the solutions.

$x - \frac{1}{2} + \frac{1}{2} = \frac{1}{2} \pm \frac{5}{2} x = \frac{1}{2} - \frac{5}{2} or x = \frac{1}{2} + \frac{5}{2} x = - 2 or x = 3$

Therefore, the solutions of the equation are $- 2$ and 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 each equation by completing the square.
$x^{2} - x - 6 = 0$

Short Answer

Step by step solution

Step 1. Complete the square

Step 2. Take the square root of each side

Step 3. Write the solutions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Probability and Statistics

Decision Maths

Mechanics Maths

Theoretical and Mathematical Physics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve each equation by completing the square.x2−x−6=0

Short Answer

Step by step solution

Step 1. Complete the square

Step 2. Take the square root of each side

Step 3. Write the solutions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Probability and Statistics

Decision Maths

Mechanics Maths

Theoretical and Mathematical Physics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve each equation by completing the square.
$x^{2} - x - 6 = 0$