Solve Using the Square Root Property (x-4)^2=169

${(x - 4)}^{2} = 169$

Step 1

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

$x - 4 = \pm \sqrt{169}$

Step 2

Simplify $\pm \sqrt{169}$ .

Rewrite $169$ as $13^{2}$ .

$x - 4 = \pm \sqrt{13^{2}}$

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

$x - 4 = \pm 13$

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.

$x - 4 = 13$

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

Add $4$ to both sides of the equation.

$x = 13 + 4$

Add $13$ and $4$ .

$x = 17$

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

$x - 4 = - 13$

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

Add $4$ to both sides of the equation.

$x = - 13 + 4$

Add $- 13$ and $4$ .

$x = - 9$

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

$x = 17, - 9$