Solve for c 7^2+12^2=c^2

$7^{2} + 12^{2} = c^{2}$

Step 1

Rewrite the equation as $c^{2} = 7^{2} + 12^{2}$ .

$c^{2} = 7^{2} + 12^{2}$

Step 2

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

$c = \pm \sqrt{7^{2} + 12^{2}}$

Step 3

Simplify $\pm \sqrt{7^{2} + 12^{2}}$ .

Raise $7$ to the power of $2$ .

$c = \pm \sqrt{49 + 12^{2}}$

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

$c = \pm \sqrt{49 + 144}$

Add $49$ and $144$ .

$c = \pm \sqrt{193}$

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.

$c = \sqrt{193}$

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

$c = - \sqrt{193}$

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

$c = \sqrt{193}, - \sqrt{193}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$c = \sqrt{193}, - \sqrt{193}$

Decimal Form:

$c = 13.89244398 \dots, - 13.89244398 \dots$