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

${(x + 3)}^{2} = - 17$

Step 1

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

$x + 3 = \pm \sqrt{- 17}$

Step 2

Simplify $\pm \sqrt{- 17}$ .

Rewrite $- 17$ as $- 1 (17)$ .

$x + 3 = \pm \sqrt{- 1 (17)}$

Rewrite $\sqrt{- 1 (17)}$ as $\sqrt{- 1} \cdot \sqrt{17}$ .

$x + 3 = \pm \sqrt{- 1} \cdot \sqrt{17}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x + 3 = \pm i \sqrt{17}$

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.

$x + 3 = i \sqrt{17}$

Subtract $3$ from both sides of the equation.

$x = i \sqrt{17} - 3$

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

$x + 3 = - i \sqrt{17}$

Subtract $3$ from both sides of the equation.

$x = - i \sqrt{17} - 3$

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

$x = i \sqrt{17} - 3, - i \sqrt{17} - 3$