Solve Using the Square Root Property (x-5)^2=8

${(x - 5)}^{2} = 8$

Step 1

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

$x - 5 = \pm \sqrt{8}$

Step 2

Simplify $\pm \sqrt{8}$ .

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$x - 5 = \pm \sqrt{4 (2)}$

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

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

Pull terms out from under the radical.

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

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.

$x - 5 = 2 \sqrt{2}$

Add $5$ to both sides of the equation.

$x = 2 \sqrt{2} + 5$

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

$x - 5 = - 2 \sqrt{2}$

Add $5$ to both sides of the equation.

$x = - 2 \sqrt{2} + 5$

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

$x = 2 \sqrt{2} + 5, - 2 \sqrt{2} + 5$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = 2 \sqrt{2} + 5, - 2 \sqrt{2} + 5$

Decimal Form:

$x = 7.82842712 \dots, 2.17157287 \dots$