Solve Using the Square Root Property -3(y+4)^2=-147

$- 3 {(y + 4)}^{2} = - 147$

Step 1

Divide each term in $- 3 {(y + 4)}^{2} = - 147$ by $- 3$ and simplify.

Divide each term in $- 3 {(y + 4)}^{2} = - 147$ by $- 3$ .

$\frac{- 3 {(y + 4)}^{2}}{- 3} = \frac{- 147}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 {(y + 4)}^{2}}{- 3} = \frac{- 147}{- 3}$

Divide ${(y + 4)}^{2}$ by $1$ .

${(y + 4)}^{2} = \frac{- 147}{- 3}$

Simplify the right side.

Divide $- 147$ by $- 3$ .

${(y + 4)}^{2} = 49$

Step 2

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

$y + 4 = \pm \sqrt{49}$

Step 3

Simplify $\pm \sqrt{49}$ .

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

$y + 4 = \pm \sqrt{7^{2}}$

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

$y + 4 = \pm 7$

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.

$y + 4 = 7$

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

Subtract $4$ from both sides of the equation.

$y = 7 - 4$

Subtract $4$ from $7$ .

$y = 3$

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

$y + 4 = - 7$

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

Subtract $4$ from both sides of the equation.

$y = - 7 - 4$

Subtract $4$ from $- 7$ .

$y = - 11$

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

$y = 3, - 11$