Solve Using the Square Root Property -3(y+8)^2=-300

$- 3 {(y + 8)}^{2} = - 300$

Step 1

Divide each term in $- 3 {(y + 8)}^{2} = - 300$ by $- 3$ and simplify.

Divide each term in $- 3 {(y + 8)}^{2} = - 300$ by $- 3$ .

$\frac{- 3 {(y + 8)}^{2}}{- 3} = \frac{- 300}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 {(y + 8)}^{2}}{- 3} = \frac{- 300}{- 3}$

Divide ${(y + 8)}^{2}$ by $1$ .

${(y + 8)}^{2} = \frac{- 300}{- 3}$

Simplify the right side.

Divide $- 300$ by $- 3$ .

${(y + 8)}^{2} = 100$

Step 2

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

$y + 8 = \pm \sqrt{100}$

Step 3

Simplify $\pm \sqrt{100}$ .

Rewrite $100$ as $10^{2}$ .

$y + 8 = \pm \sqrt{10^{2}}$

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

$y + 8 = \pm 10$

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.

$y + 8 = 10$

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

Subtract $8$ from both sides of the equation.

$y = 10 - 8$

Subtract $8$ from $10$ .

$y = 2$

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

$y + 8 = - 10$

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

Subtract $8$ from both sides of the equation.

$y = - 10 - 8$

Subtract $8$ from $- 10$ .

$y = - 18$

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

$y = 2, - 18$