Solve Using the Square Root Property 2(x+2)^2=72

$2 {(x + 2)}^{2} = 72$

Step 1

Divide each term in $2 {(x + 2)}^{2} = 72$ by $2$ and simplify.

Divide each term in $2 {(x + 2)}^{2} = 72$ by $2$ .

$\frac{2 {(x + 2)}^{2}}{2} = \frac{72}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 {(x + 2)}^{2}}{2} = \frac{72}{2}$

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

${(x + 2)}^{2} = \frac{72}{2}$

Simplify the right side.

Divide $72$ by $2$ .

${(x + 2)}^{2} = 36$

Step 2

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

$x + 2 = \pm \sqrt{36}$

Step 3

Simplify $\pm \sqrt{36}$ .

Rewrite $36$ as $6^{2}$ .

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

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

$x + 2 = \pm 6$

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.

$x + 2 = 6$

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

Subtract $2$ from both sides of the equation.

$x = 6 - 2$

Subtract $2$ from $6$ .

$x = 4$

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

$x + 2 = - 6$

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

Subtract $2$ from both sides of the equation.

$x = - 6 - 2$

Subtract $2$ from $- 6$ .

$x = - 8$

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

$x = 4, - 8$