Solve Using the Square Root Property (x-5)^2+2=11

${(x - 5)}^{2} + 2 = 11$

Step 1

Subtract $2$ from both sides of the equation.

${(x - 5)}^{2} = 11 - 2$

Step 2

Subtract $2$ from $11$ .

${(x - 5)}^{2} = 9$

Step 3

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

$x - 5 = \pm \sqrt{9}$

Step 4

Simplify $\pm \sqrt{9}$ .

Rewrite $9$ as $3^{2}$ .

$x - 5 = \pm \sqrt{3^{2}}$

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

$x - 5 = \pm 3$

Step 5

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.

$x - 5 = 3$

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

Add $5$ to both sides of the equation.

$x = 3 + 5$

Add $3$ and $5$ .

$x = 8$

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

$x - 5 = - 3$

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

Add $5$ to both sides of the equation.

$x = - 3 + 5$

Add $- 3$ and $5$ .

$x = 2$

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

$x = 8, 2$