Solve Using the Square Root Property (z+3)^2=17

${(z + 3)}^{2} = 17$

Step 1

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

$z + 3 = \pm \sqrt{17}$

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.

$z + 3 = \sqrt{17}$

Subtract $3$ from both sides of the equation.

$z = \sqrt{17} - 3$

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

$z + 3 = - \sqrt{17}$

Subtract $3$ from both sides of the equation.

$z = - \sqrt{17} - 3$

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

$z = \sqrt{17} - 3, - \sqrt{17} - 3$

Step 3

The result can be shown in multiple forms.

Exact Form:

$z = \sqrt{17} - 3, - \sqrt{17} - 3$

Decimal Form:

$z = 1.12310562 \dots, - 7.12310562 \dots$