Solve Using the Square Root Property -2(x+7)^2=-162

$- 2 {(x + 7)}^{2} = - 162$

Step 1

Divide each term in $- 2 {(x + 7)}^{2} = - 162$ by $- 2$ and simplify.

Divide each term in $- 2 {(x + 7)}^{2} = - 162$ by $- 2$ .

$\frac{- 2 {(x + 7)}^{2}}{- 2} = \frac{- 162}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 {(x + 7)}^{2}}{- 2} = \frac{- 162}{- 2}$

Divide ${(x + 7)}^{2}$ by $1$ .

${(x + 7)}^{2} = \frac{- 162}{- 2}$

Simplify the right side.

Divide $- 162$ by $- 2$ .

${(x + 7)}^{2} = 81$

Step 2

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

$x + 7 = \pm \sqrt{81}$

Step 3

Simplify $\pm \sqrt{81}$ .

Rewrite $81$ as $9^{2}$ .

$x + 7 = \pm \sqrt{9^{2}}$

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

$x + 7 = \pm 9$

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.

$x + 7 = 9$

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

Subtract $7$ from both sides of the equation.

$x = 9 - 7$

Subtract $7$ from $9$ .

$x = 2$

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

$x + 7 = - 9$

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

Subtract $7$ from both sides of the equation.

$x = - 9 - 7$

Subtract $7$ from $- 9$ .

$x = - 16$

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

$x = 2, - 16$