Solve Using the Square Root Property (x+2)^2=13

${(x + 2)}^{2} = 13$

Step 1

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

$x + 2 = \pm \sqrt{13}$

Step 2

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.

$x + 2 = \sqrt{13}$

Subtract $2$ from both sides of the equation.

$x = \sqrt{13} - 2$

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

$x + 2 = - \sqrt{13}$

Subtract $2$ from both sides of the equation.

$x = - \sqrt{13} - 2$

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

$x = \sqrt{13} - 2, - \sqrt{13} - 2$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{13} - 2, - \sqrt{13} - 2$

Decimal Form:

$x = 1.60555127 \dots, - 5.60555127 \dots$