Solve Using the Square Root Property (x-12)^2=36

${(x - 12)}^{2} = 36$

Step 1

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

$x - 12 = \pm \sqrt{36}$

Step 2

Simplify $\pm \sqrt{36}$ .

Rewrite $36$ as $6^{2}$ .

$x - 12 = \pm \sqrt{6^{2}}$

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

$x - 12 = \pm 6$

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.

$x - 12 = 6$

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

Add $12$ to both sides of the equation.

$x = 6 + 12$

Add $6$ and $12$ .

$x = 18$

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

$x - 12 = - 6$

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

Add $12$ to both sides of the equation.

$x = - 6 + 12$

Add $- 6$ and $12$ .

$x = 6$

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

$x = 18, 6$