Solve Using the Square Root Property (x-4)^2=81

${(x - 4)}^{2} = 81$

Step 1

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

$x - 4 = \pm \sqrt{81}$

Step 2

Simplify $\pm \sqrt{81}$ .

Rewrite $81$ as $9^{2}$ .

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

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

$x - 4 = \pm 9$

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.

$x - 4 = 9$

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

Add $4$ to both sides of the equation.

$x = 9 + 4$

Add $9$ and $4$ .

$x = 13$

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

$x - 4 = - 9$

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

Add $4$ to both sides of the equation.

$x = - 9 + 4$

Add $- 9$ and $4$ .

$x = - 5$

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

$x = 13, - 5$