Solve Using the Square Root Property -2(x+6)^2=-200

$- 2 {(x + 6)}^{2} = - 200$

Step 1

Divide each term in $- 2 {(x + 6)}^{2} = - 200$ by $- 2$ and simplify.

Divide each term in $- 2 {(x + 6)}^{2} = - 200$ by $- 2$ .

$\frac{- 2 {(x + 6)}^{2}}{- 2} = \frac{- 200}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 {(x + 6)}^{2}}{- 2} = \frac{- 200}{- 2}$

Divide ${(x + 6)}^{2}$ by $1$ .

${(x + 6)}^{2} = \frac{- 200}{- 2}$

Simplify the right side.

Divide $- 200$ by $- 2$ .

${(x + 6)}^{2} = 100$

Step 2

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

$x + 6 = \pm \sqrt{100}$

Step 3

Simplify $\pm \sqrt{100}$ .

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

$x + 6 = \pm \sqrt{10^{2}}$

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

$x + 6 = \pm 10$

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.

$x + 6 = 10$

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

Subtract $6$ from both sides of the equation.

$x = 10 - 6$

Subtract $6$ from $10$ .

$x = 4$

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

$x + 6 = - 10$

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

Subtract $6$ from both sides of the equation.

$x = - 10 - 6$

Subtract $6$ from $- 10$ .

$x = - 16$

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

$x = 4, - 16$