Solve Using the Square Root Property (x+5)^2=325

${(x + 5)}^{2} = 325$

Step 1

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

$x + 5 = \pm \sqrt{325}$

Step 2

Simplify $\pm \sqrt{325}$ .

Rewrite $325$ as $5^{2} \cdot 13$ .

Factor $25$ out of $325$ .

$x + 5 = \pm \sqrt{25 (13)}$

Rewrite $25$ as $5^{2}$ .

$x + 5 = \pm \sqrt{5^{2} \cdot 13}$

Pull terms out from under the radical.

$x + 5 = \pm 5 \sqrt{13}$

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.

$x + 5 = 5 \sqrt{13}$

Subtract $5$ from both sides of the equation.

$x = 5 \sqrt{13} - 5$

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

$x + 5 = - 5 \sqrt{13}$

Subtract $5$ from both sides of the equation.

$x = - 5 \sqrt{13} - 5$

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

$x = 5 \sqrt{13} - 5, - 5 \sqrt{13} - 5$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = 5 \sqrt{13} - 5, - 5 \sqrt{13} - 5$

Decimal Form:

$x = 13.02775637 \dots, - 23.02775637 \dots$