Solve Using the Square Root Property (x-9)^2=16

${(x - 9)}^{2} = 16$

Step 1

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

$x - 9 = \pm \sqrt{16}$

Step 2

Simplify $\pm \sqrt{16}$ .

Rewrite $16$ as $4^{2}$ .

$x - 9 = \pm \sqrt{4^{2}}$

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

$x - 9 = \pm 4$

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.

$x - 9 = 4$

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

Add $9$ to both sides of the equation.

$x = 4 + 9$

Add $4$ and $9$ .

$x = 13$

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

$x - 9 = - 4$

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

Add $9$ to both sides of the equation.

$x = - 4 + 9$

Add $- 4$ and $9$ .

$x = 5$

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

$x = 13, 5$