Solve Using the Square Root Property 2(x+4)^2=40

$2 {(x + 4)}^{2} = 40$

Step 1

Divide each term in $2 {(x + 4)}^{2} = 40$ by $2$ and simplify.

Divide each term in $2 {(x + 4)}^{2} = 40$ by $2$ .

$\frac{2 {(x + 4)}^{2}}{2} = \frac{40}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 {(x + 4)}^{2}}{2} = \frac{40}{2}$

Divide ${(x + 4)}^{2}$ by $1$ .

${(x + 4)}^{2} = \frac{40}{2}$

Simplify the right side.

Divide $40$ by $2$ .

${(x + 4)}^{2} = 20$

Step 2

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

$x + 4 = \pm \sqrt{20}$

Step 3

Simplify $\pm \sqrt{20}$ .

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$x + 4 = \pm \sqrt{4 (5)}$

Rewrite $4$ as $2^{2}$ .

$x + 4 = \pm \sqrt{2^{2} \cdot 5}$

Pull terms out from under the radical.

$x + 4 = \pm 2 \sqrt{5}$

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.

$x + 4 = 2 \sqrt{5}$

Subtract $4$ from both sides of the equation.

$x = 2 \sqrt{5} - 4$

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

$x + 4 = - 2 \sqrt{5}$

Subtract $4$ from both sides of the equation.

$x = - 2 \sqrt{5} - 4$

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

$x = 2 \sqrt{5} - 4, - 2 \sqrt{5} - 4$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 2 \sqrt{5} - 4, - 2 \sqrt{5} - 4$

Decimal Form:

$x = 0.47213595 \dots, - 8.47213595 \dots$