Solve Using the Square Root Property (y+2)^2+124=0

${(y + 2)}^{2} + 124 = 0$

Step 1

Subtract $124$ from both sides of the equation.

${(y + 2)}^{2} = - 124$

Step 2

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

$y + 2 = \pm \sqrt{- 124}$

Step 3

Simplify $\pm \sqrt{- 124}$ .

Rewrite $- 124$ as $- 1 (124)$ .

$y + 2 = \pm \sqrt{- 1 (124)}$

Rewrite $\sqrt{- 1 (124)}$ as $\sqrt{- 1} \cdot \sqrt{124}$ .

$y + 2 = \pm \sqrt{- 1} \cdot \sqrt{124}$

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

$y + 2 = \pm i \cdot \sqrt{124}$

Rewrite $124$ as $2^{2} \cdot 31$ .

Factor $4$ out of $124$ .

$y + 2 = \pm i \cdot \sqrt{4 (31)}$

Rewrite $4$ as $2^{2}$ .

$y + 2 = \pm i \cdot \sqrt{2^{2} \cdot 31}$

Pull terms out from under the radical.

$y + 2 = \pm i \cdot (2 \sqrt{31})$

Move $2$ to the left of $i$ .

$y + 2 = \pm 2 i \sqrt{31}$

Step 4

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.

$y + 2 = 2 i \sqrt{31}$

Subtract $2$ from both sides of the equation.

$y = 2 i \sqrt{31} - 2$

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

$y + 2 = - 2 i \sqrt{31}$

Subtract $2$ from both sides of the equation.

$y = - 2 i \sqrt{31} - 2$

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

$y = 2 i \sqrt{31} - 2, - 2 i \sqrt{31} - 2$