Solve for c 18^2+12^2=c^2

$18^{2} + 12^{2} = c^{2}$

Step 1

Rewrite the equation as $c^{2} = 18^{2} + 12^{2}$ .

$c^{2} = 18^{2} + 12^{2}$

Step 2

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

$c = \pm \sqrt{18^{2} + 12^{2}}$

Step 3

Simplify $\pm \sqrt{18^{2} + 12^{2}}$ .

Raise $18$ to the power of $2$ .

$c = \pm \sqrt{324 + 12^{2}}$

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

$c = \pm \sqrt{324 + 144}$

Add $324$ and $144$ .

$c = \pm \sqrt{468}$

Rewrite $468$ as $6^{2} \cdot 13$ .

Factor $36$ out of $468$ .

$c = \pm \sqrt{36 (13)}$

Rewrite $36$ as $6^{2}$ .

$c = \pm \sqrt{6^{2} \cdot 13}$

Pull terms out from under the radical.

$c = \pm 6 \sqrt{13}$

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.

$c = 6 \sqrt{13}$

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

$c = - 6 \sqrt{13}$

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

$c = 6 \sqrt{13}, - 6 \sqrt{13}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$c = 6 \sqrt{13}, - 6 \sqrt{13}$

Decimal Form:

$c = 21.63330765 \dots, - 21.63330765 \dots$