Solve for a 17^2=a^2+15^2

$17^{2} = a^{2} + 15^{2}$

Step 1

Rewrite the equation as $a^{2} + 15^{2} = 17^{2}$ .

$a^{2} + 15^{2} = 17^{2}$

Step 2

Raise $15$ to the power of $2$ .

$a^{2} + 225 = 17^{2}$

Step 3

Raise $17$ to the power of $2$ .

$a^{2} + 225 = 289$

Step 4

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

Subtract $225$ from both sides of the equation.

$a^{2} = 289 - 225$

Subtract $225$ from $289$ .

$a^{2} = 64$

Step 5

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

$a = \pm \sqrt{64}$

Step 6

Simplify $\pm \sqrt{64}$ .

Rewrite $64$ as $8^{2}$ .

$a = \pm \sqrt{8^{2}}$

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

$a = \pm 8$

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.

$a = 8$

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

$a = - 8$

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

$a = 8, - 8$