Solve Using the Square Root Property -3(y+9)^2=-27

$- 3 {(y + 9)}^{2} = - 27$

Step 1

Divide each term in $- 3 {(y + 9)}^{2} = - 27$ by $- 3$ and simplify.

Divide each term in $- 3 {(y + 9)}^{2} = - 27$ by $- 3$ .

$\frac{- 3 {(y + 9)}^{2}}{- 3} = \frac{- 27}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 {(y + 9)}^{2}}{- 3} = \frac{- 27}{- 3}$

Divide ${(y + 9)}^{2}$ by $1$ .

${(y + 9)}^{2} = \frac{- 27}{- 3}$

Simplify the right side.

Divide $- 27$ by $- 3$ .

${(y + 9)}^{2} = 9$

Step 2

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

$y + 9 = \pm \sqrt{9}$

Step 3

Simplify $\pm \sqrt{9}$ .

Rewrite $9$ as $3^{2}$ .

$y + 9 = \pm \sqrt{3^{2}}$

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

$y + 9 = \pm 3$

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.

$y + 9 = 3$

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

Subtract $9$ from both sides of the equation.

$y = 3 - 9$

Subtract $9$ from $3$ .

$y = - 6$

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

$y + 9 = - 3$

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

Subtract $9$ from both sides of the equation.

$y = - 3 - 9$

Subtract $9$ from $- 3$ .

$y = - 12$

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

$y = - 6, - 12$