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

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

Step 1

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

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

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

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

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

Simplify the right side.

Divide $- 147$ by $- 3$ .

${(x + 2)}^{2} = 49$

Step 2

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

$x + 2 = \pm \sqrt{49}$

Step 3

Simplify $\pm \sqrt{49}$ .

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

$x + 2 = \pm \sqrt{7^{2}}$

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

$x + 2 = \pm 7$

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.

$x + 2 = 7$

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

Subtract $2$ from both sides of the equation.

$x = 7 - 2$

Subtract $2$ from $7$ .

$x = 5$

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

$x + 2 = - 7$

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

Subtract $2$ from both sides of the equation.

$x = - 7 - 2$

Subtract $2$ from $- 7$ .

$x = - 9$

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

$x = 5, - 9$