Find the Roots (Zeros) (x+8)^2-7=0

${(x + 8)}^{2} - 7 = 0$

Step 1

Add $7$ to both sides of the equation.

${(x + 8)}^{2} = 7$

Step 2

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

$x + 8 = \pm \sqrt{7}$

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.

$x + 8 = \sqrt{7}$

Subtract $8$ from both sides of the equation.

$x = \sqrt{7} - 8$

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

$x + 8 = - \sqrt{7}$

Subtract $8$ from both sides of the equation.

$x = - \sqrt{7} - 8$

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

$x = \sqrt{7} - 8, - \sqrt{7} - 8$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{7} - 8, - \sqrt{7} - 8$

Decimal Form:

$x = - 5.35424868 \dots, - 10.64575131 \dots$

Step 5