Solve Using the Square Root Property (x-6)^2=144

${(x - 6)}^{2} = 144$

Step 1

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

$x - 6 = \pm \sqrt{144}$

Step 2

Simplify $\pm \sqrt{144}$ .

Rewrite $144$ as $12^{2}$ .

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

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

$x - 6 = \pm 12$

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.

$x - 6 = 12$

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

Add $6$ to both sides of the equation.

$x = 12 + 6$

Add $12$ and $6$ .

$x = 18$

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

$x - 6 = - 12$

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

Add $6$ to both sides of the equation.

$x = - 12 + 6$

Add $- 12$ and $6$ .

$x = - 6$

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

$x = 18, - 6$