Solve Using the Square Root Property (x-9)^2=4

${(x - 9)}^{2} = 4$

Step 1

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

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

Step 2

Simplify $\pm \sqrt{4}$ .

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

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

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

$x - 9 = \pm 2$

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.

$x - 9 = 2$

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

Add $9$ to both sides of the equation.

$x = 2 + 9$

Add $2$ and $9$ .

$x = 11$

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

$x - 9 = - 2$

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

Add $9$ to both sides of the equation.

$x = - 2 + 9$

Add $- 2$ and $9$ .

$x = 7$

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

$x = 11, 7$