Solve Using the Square Root Property (x+15)^2-10=0

${(x + 15)}^{2} - 10 = 0$

Step 1

Add $10$ to both sides of the equation.

${(x + 15)}^{2} = 10$

Step 2

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

$x + 15 = \pm \sqrt{10}$

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.

$x + 15 = \sqrt{10}$

Subtract $15$ from both sides of the equation.

$x = \sqrt{10} - 15$

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

$x + 15 = - \sqrt{10}$

Subtract $15$ from both sides of the equation.

$x = - \sqrt{10} - 15$

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

$x = \sqrt{10} - 15, - \sqrt{10} - 15$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{10} - 15, - \sqrt{10} - 15$

Decimal Form:

$x = - 11.83772233 \dots, - 18.16227766 \dots$