Solve for c 8^2+c^2=14^2

$8^{2} + c^{2} = 14^{2}$

Step 1

Raise $8$ to the power of $2$ .

$64 + c^{2} = 14^{2}$

Step 2

Raise $14$ to the power of $2$ .

$64 + c^{2} = 196$

Step 3

Move all terms not containing $c$ to the right side of the equation.

Subtract $64$ from both sides of the equation.

$c^{2} = 196 - 64$

Subtract $64$ from $196$ .

$c^{2} = 132$

Step 4

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$c = \pm \sqrt{132}$

Step 5

Simplify $\pm \sqrt{132}$ .

Rewrite $132$ as $2^{2} \cdot 33$ .

Factor $4$ out of $132$ .

$c = \pm \sqrt{4 (33)}$

Rewrite $4$ as $2^{2}$ .

$c = \pm \sqrt{2^{2} \cdot 33}$

Pull terms out from under the radical.

$c = \pm 2 \sqrt{33}$

Step 6

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$c = 2 \sqrt{33}$

Next, use the negative value of the $\pm$ to find the second solution.

$c = - 2 \sqrt{33}$

The complete solution is the result of both the positive and negative portions of the solution.

$c = 2 \sqrt{33}, - 2 \sqrt{33}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$c = 2 \sqrt{33}, - 2 \sqrt{33}$

Decimal Form:

$c = 11.48912529 \dots, - 11.48912529 \dots$