Solve Using the Square Root Property 4(x+2)^2=36

$4 {(x + 2)}^{2} = 36$

Step 1

Divide each term in $4 {(x + 2)}^{2} = 36$ by $4$ and simplify.

Divide each term in $4 {(x + 2)}^{2} = 36$ by $4$ .

$\frac{4 {(x + 2)}^{2}}{4} = \frac{36}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 {(x + 2)}^{2}}{4} = \frac{36}{4}$

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

${(x + 2)}^{2} = \frac{36}{4}$

Simplify the right side.

Divide $36$ by $4$ .

${(x + 2)}^{2} = 9$

Step 2

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

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

Step 3

Simplify $\pm \sqrt{9}$ .

Rewrite $9$ as $3^{2}$ .

$x + 2 = \pm \sqrt{3^{2}}$

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

$x + 2 = \pm 3$

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.

$x + 2 = 3$

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

Subtract $2$ from both sides of the equation.

$x = 3 - 2$

Subtract $2$ from $3$ .

$x = 1$

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

$x + 2 = - 3$

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

Subtract $2$ from both sides of the equation.

$x = - 3 - 2$

Subtract $2$ from $- 3$ .

$x = - 5$

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

$x = 1, - 5$