Chapter 10: Q 249 (page 1236)

In the following exercises, solve by completing the square.
$x^{2} - 4 x = 32$

Short Answer

Expert verified

The solutions are $x = - 4 a n d x = 8 .$

Step by step solution

Given information.

Given equation $x^{2} - 4 x = 32$

Make the perfect square.

Adding 4 to both sides of the equation.

$x^{2} - 4 x + 4 = 32 + 4 x^{2} - 4 x = 36$

Writing it as a binomial square.

$x^{2} - 2 \times x \times 2 + 2^{2} = 36 {(x - 2)}^{2} = 36$

Use the square root property.

$x - 2 = \pm \sqrt{36} x - 2 = \pm \sqrt{6^{2}} x - 2 = \pm 6$

The two equations are $x - 2 = 6 a n d x - 2 = - 6 .$

Solve both equations for x.

$x - 2 = - 6 x = - 6 + 2 x = - 4 O r x - 2 = 6 x = 6 + 2 x = 8$

Therefore, the solutions are $x = 8 a n d x = - 4 .$

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In the following exercises, solve by completing the square.
$x^{2} - 4 x = 32$

Short Answer

Step by step solution

Given information.

Make the perfect square.

Use the square root property.

Solve both equations for x.

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In the following exercises, solve by completing the square.x2-4x=32

Short Answer

Step by step solution

Given information.

Make the perfect square.

Use the square root property.

Solve both equations for x.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Pure Maths

Discrete Mathematics

Mechanics Maths

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, solve by completing the square.
$x^{2} - 4 x = 32$