Solve Using the Square Root Property (x-8)^2=9

${(x - 8)}^{2} = 9$

Step 1

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

$x - 8 = \pm \sqrt{9}$

Step 2

Simplify $\pm \sqrt{9}$ .

Rewrite $9$ as $3^{2}$ .

$x - 8 = \pm \sqrt{3^{2}}$

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

$x - 8 = \pm 3$

Step 3

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.

$x - 8 = 3$

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

Add $8$ to both sides of the equation.

$x = 3 + 8$

Add $3$ and $8$ .

$x = 11$

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

$x - 8 = - 3$

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

Add $8$ to both sides of the equation.

$x = - 3 + 8$

Add $- 3$ and $8$ .

$x = 5$

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

$x = 11, 5$