Solve Using the Square Root Property (z+7)^2=13

${(z + 7)}^{2} = 13$

Step 1

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

$z + 7 = \pm \sqrt{13}$

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.

$z + 7 = \sqrt{13}$

Subtract $7$ from both sides of the equation.

$z = \sqrt{13} - 7$

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

$z + 7 = - \sqrt{13}$

Subtract $7$ from both sides of the equation.

$z = - \sqrt{13} - 7$

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

$z = \sqrt{13} - 7, - \sqrt{13} - 7$

Step 3

The result can be shown in multiple forms.

Exact Form:

$z = \sqrt{13} - 7, - \sqrt{13} - 7$

Decimal Form:

$z = - 3.39444872 \dots, - 10.60555127 \dots$