Find the Roots (Zeros) (x+7)^2-11=0

${(x + 7)}^{2} - 11 = 0$

Step 1

Add $11$ to both sides of the equation.

${(x + 7)}^{2} = 11$

Step 2

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

$x + 7 = \pm \sqrt{11}$

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.

$x + 7 = \sqrt{11}$

Subtract $7$ from both sides of the equation.

$x = \sqrt{11} - 7$

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

$x + 7 = - \sqrt{11}$

Subtract $7$ from both sides of the equation.

$x = - \sqrt{11} - 7$

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

$x = \sqrt{11} - 7, - \sqrt{11} - 7$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{11} - 7, - \sqrt{11} - 7$

Decimal Form:

$x = - 3.68337520 \dots, - 10.31662479 \dots$

Step 5