Chapter 10: Q 247 (page 1236)

In the following exercises, solve by completing the square.
$c^{2} + 20 c = 21$

Short Answer

Expert verified

The solutions are $c = 1 a n d c = - 21 .$

Step by step solution

Given information

The given equation is: $c^{2} + 20 c = 21$

Make the perfect square.

Adding 100 to both sides of the given equation.

$c^{2} + 20 c + 100 = 21 + 100 c^{2} + 20 c + 100 = 121$

Writing it as a binomial square.

role="math" localid="1653497925300" ${(c)}^{2} + 2 \times c \times 10 + {(10)}^{2} = 121 {(c + 10)}^{2} = 121$

Use the square root property.

$c + 10 = \pm \sqrt{121} c + 10 = \pm \sqrt{11^{2}} c + 10 = \pm 11$

The two equations are $c + 10 = - 11 a n d c + 10 = 11 .$

Solve both equations forc.

$c + 10 = - 11 c = - 11 - 10 c = - 21 O r c + 10 = 11 c = 11 - 10 c = 1$

Therefore, the two solutions are $c = 1 a n d c = - 21 .$

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In the following exercises, solve by completing the square.
$c^{2} + 20 c = 21$

Short Answer

Step by step solution

Given information

Make the perfect square.

Use the square root property.

Solve both equations forc.

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In the following exercises, solve by completing the square.c2+20c=21

Short Answer

Step by step solution

Given information

Make the perfect square.

Use the square root property.

Solve both equations forc.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Mechanics Maths

Statistics

Probability and Statistics

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, solve by completing the square.
$c^{2} + 20 c = 21$