Solve for c 5^2+12^2=c^2

$5^{2} + 12^{2} = c^{2}$

Step 1

Rewrite the equation as $c^{2} = 5^{2} + 12^{2}$ .

$c^{2} = 5^{2} + 12^{2}$

Step 2

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

$c = \pm \sqrt{5^{2} + 12^{2}}$

Step 3

Simplify $\pm \sqrt{5^{2} + 12^{2}}$ .

Raise $5$ to the power of $2$ .

$c = \pm \sqrt{25 + 12^{2}}$

Raise $12$ to the power of $2$ .

$c = \pm \sqrt{25 + 144}$

Add $25$ and $144$ .

$c = \pm \sqrt{169}$

Rewrite $169$ as $13^{2}$ .

$c = \pm \sqrt{13^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$c = \pm 13$

Step 4

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.

$c = 13$

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

$c = - 13$

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

$c = 13, - 13$