Chapter 10: Q 73 (page 1181)

Solve the equation by completing square method.
$c^{2} - 12 c = 13$

Short Answer

Expert verified

The solutions are $c = - 1, c = 13$ .

Step by step solution

Given Information.

The Given equation is $c^{2} - 12 c = 13$ .

Isolate the variable terms on one side and the constant terms on the other.

The variable terms are on the left side.

$c^{2} - 12 c = 13$

The coefficient of $c$ is $- 12$ .

So, $b = - 12$

Find 12b2and add to the both sides of equation.

$= {(\frac{1}{2} (- 12))}^{2} = {(- 6)}^{2} = 36$

Add $36$ both sides.

$c^{2} - 12 c + 36 = 13 + 36 c^{2} - 12 c + 36 = 49$

Factor the perfect square trinomial as a binomial square.

$(c - 6)^{2} = 49$

Use the square root property.

$c - 6 = \pm \sqrt{49} c - 6 = \pm 7 c = 6 \pm 7$

Rewrite to show two solutions.

$c = 6 + 7 = 13 c = 6 - 7 = - 1$

The solutions are $c = - 1, c = 13$ .

Check the solutions.

Substitute $c = - 1$

$c^{2} - 12 c = 13 (- 1)^{2} - 12 (- 1) \overset{?}{=} 13 1 + 12 \overset{?}{=} 13 13 = 13 T r u e$

Substitute $c = 13$

$c^{2} - 12 c = 13 (13)^{2} - 12 (13) \overset{?}{=} 13 169 - 156 \overset{?}{=} 13 13 = 13 T r u e$

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Solve the equation by completing square method.
$c^{2} - 12 c = 13$

Short Answer

Step by step solution

Given Information.

Isolate the variable terms on one side and the constant terms on the other.

Find 12b2and add to the both sides of equation.

Factor the perfect square trinomial as a binomial square.

Check the solutions.

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Solve the equation by completing square method.c2-12c=13

Short Answer

Step by step solution

Given Information.

Isolate the variable terms on one side and the constant terms on the other.

Find 12b2and add to the both sides of equation.

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

Discrete Mathematics

Pure Maths

Geometry

Theoretical and Mathematical Physics

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Solve the equation by completing square method.
$c^{2} - 12 c = 13$