Solve Using the Square Root Property -2(y+7)^2=-128

$- 2 {(y + 7)}^{2} = - 128$

Step 1

Divide each term in $- 2 {(y + 7)}^{2} = - 128$ by $- 2$ and simplify.

Divide each term in $- 2 {(y + 7)}^{2} = - 128$ by $- 2$ .

$\frac{- 2 {(y + 7)}^{2}}{- 2} = \frac{- 128}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 {(y + 7)}^{2}}{- 2} = \frac{- 128}{- 2}$

Divide ${(y + 7)}^{2}$ by $1$ .

${(y + 7)}^{2} = \frac{- 128}{- 2}$

Simplify the right side.

Divide $- 128$ by $- 2$ .

${(y + 7)}^{2} = 64$

Step 2

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

$y + 7 = \pm \sqrt{64}$

Step 3

Simplify $\pm \sqrt{64}$ .

Rewrite $64$ as $8^{2}$ .

$y + 7 = \pm \sqrt{8^{2}}$

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

$y + 7 = \pm 8$

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.

$y + 7 = 8$

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

Subtract $7$ from both sides of the equation.

$y = 8 - 7$

Subtract $7$ from $8$ .

$y = 1$

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

$y + 7 = - 8$

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

Subtract $7$ from both sides of the equation.

$y = - 8 - 7$

Subtract $7$ from $- 8$ .

$y = - 15$

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

$y = 1, - 15$