Solve Using the Square Root Property (y+2)^2+49=0

${(y + 2)}^{2} + 49 = 0$

Step 1

Subtract $49$ from both sides of the equation.

${(y + 2)}^{2} = - 49$

Step 2

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

$y + 2 = \pm \sqrt{- 49}$

Step 3

Simplify $\pm \sqrt{- 49}$ .

Rewrite $- 49$ as $- 1 (49)$ .

$y + 2 = \pm \sqrt{- 1 (49)}$

Rewrite $\sqrt{- 1 (49)}$ as $\sqrt{- 1} \cdot \sqrt{49}$ .

$y + 2 = \pm \sqrt{- 1} \cdot \sqrt{49}$

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

$y + 2 = \pm i \cdot \sqrt{49}$

Rewrite $49$ as $7^{2}$ .

$y + 2 = \pm i \cdot \sqrt{7^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$y + 2 = \pm i \cdot 7$

Move $7$ to the left of $i$ .

$y + 2 = \pm 7 i$

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.

$y + 2 = 7 i$

Move all terms not containing $y$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$y = 7 i - 2$

Reorder $7 i$ and $- 2$ .

$y = - 2 + 7 i$

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

$y + 2 = - 7 i$

Move all terms not containing $y$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$y = - 7 i - 2$

Reorder $- 7 i$ and $- 2$ .

$y = - 2 - 7 i$

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

$y = - 2 + 7 i, - 2 - 7 i$