Solve Using the Square Root Property (y+2)^2+148=0

${(y + 2)}^{2} + 148 = 0$

Step 1

Subtract $148$ from both sides of the equation.

${(y + 2)}^{2} = - 148$

Step 2

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

$y + 2 = \pm \sqrt{- 148}$

Step 3

Simplify $\pm \sqrt{- 148}$ .

Rewrite $- 148$ as $- 1 (148)$ .

$y + 2 = \pm \sqrt{- 1 (148)}$

Rewrite $\sqrt{- 1 (148)}$ as $\sqrt{- 1} \cdot \sqrt{148}$ .

$y + 2 = \pm \sqrt{- 1} \cdot \sqrt{148}$

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

$y + 2 = \pm i \cdot \sqrt{148}$

Rewrite $148$ as $2^{2} \cdot 37$ .

Factor $4$ out of $148$ .

$y + 2 = \pm i \cdot \sqrt{4 (37)}$

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

$y + 2 = \pm i \cdot \sqrt{2^{2} \cdot 37}$

Pull terms out from under the radical.

$y + 2 = \pm i \cdot (2 \sqrt{37})$

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

$y + 2 = \pm 2 i \sqrt{37}$

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.

$y + 2 = 2 i \sqrt{37}$

Subtract $2$ from both sides of the equation.

$y = 2 i \sqrt{37} - 2$

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

$y + 2 = - 2 i \sqrt{37}$

Subtract $2$ from both sides of the equation.

$y = - 2 i \sqrt{37} - 2$

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

$y = 2 i \sqrt{37} - 2, - 2 i \sqrt{37} - 2$