Solve Using the Square Root Property (x+5)^2=10

${(x + 5)}^{2} = 10$

Step 1

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

$x + 5 = \pm \sqrt{10}$

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.

$x + 5 = \sqrt{10}$

Subtract $5$ from both sides of the equation.

$x = \sqrt{10} - 5$

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

$x + 5 = - \sqrt{10}$

Subtract $5$ from both sides of the equation.

$x = - \sqrt{10} - 5$

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

$x = \sqrt{10} - 5, - \sqrt{10} - 5$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{10} - 5, - \sqrt{10} - 5$

Decimal Form:

$x = - 1.83772233 \dots, - 8.16227766 \dots$