Solve for a 13^2=a^2+12^2

$13^{2} = a^{2} + 12^{2}$

Step 1

Rewrite the equation as $a^{2} + 12^{2} = 13^{2}$ .

$a^{2} + 12^{2} = 13^{2}$

Step 2

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

$a^{2} + 144 = 13^{2}$

Step 3

Raise $13$ to the power of $2$ .

$a^{2} + 144 = 169$

Step 4

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

Subtract $144$ from both sides of the equation.

$a^{2} = 169 - 144$

Subtract $144$ from $169$ .

$a^{2} = 25$

Step 5

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

$a = \pm \sqrt{25}$

Step 6

Simplify $\pm \sqrt{25}$ .

Rewrite $25$ as $5^{2}$ .

$a = \pm \sqrt{5^{2}}$

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

$a = \pm 5$

Step 7

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.

$a = 5$

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

$a = - 5$

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

$a = 5, - 5$