Solve Using the Square Root Property -3(y+2)^2=-75

$- 3 {(y + 2)}^{2} = - 75$

Step 1

Divide each term in $- 3 {(y + 2)}^{2} = - 75$ by $- 3$ and simplify.

Divide each term in $- 3 {(y + 2)}^{2} = - 75$ by $- 3$ .

$\frac{- 3 {(y + 2)}^{2}}{- 3} = \frac{- 75}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 {(y + 2)}^{2}}{- 3} = \frac{- 75}{- 3}$

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

${(y + 2)}^{2} = \frac{- 75}{- 3}$

Simplify the right side.

Divide $- 75$ by $- 3$ .

${(y + 2)}^{2} = 25$

Step 2

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

$y + 2 = \pm \sqrt{25}$

Step 3

Simplify $\pm \sqrt{25}$ .

Rewrite $25$ as $5^{2}$ .

$y + 2 = \pm \sqrt{5^{2}}$

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

$y + 2 = \pm 5$

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.

$y + 2 = 5$

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

Subtract $2$ from both sides of the equation.

$y = 5 - 2$

Subtract $2$ from $5$ .

$y = 3$

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

$y + 2 = - 5$

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

Subtract $2$ from both sides of the equation.

$y = - 5 - 2$

Subtract $2$ from $- 5$ .

$y = - 7$

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

$y = 3, - 7$