Solve Using the Square Root Property 2(x+7)^2=64

$2 {(x + 7)}^{2} = 64$

Step 1

Divide each term in $2 {(x + 7)}^{2} = 64$ by $2$ and simplify.

Divide each term in $2 {(x + 7)}^{2} = 64$ by $2$ .

$\frac{2 {(x + 7)}^{2}}{2} = \frac{64}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 {(x + 7)}^{2}}{2} = \frac{64}{2}$

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

${(x + 7)}^{2} = \frac{64}{2}$

Simplify the right side.

Divide $64$ by $2$ .

${(x + 7)}^{2} = 32$

Step 2

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

$x + 7 = \pm \sqrt{32}$

Step 3

Simplify $\pm \sqrt{32}$ .

Rewrite $32$ as $4^{2} \cdot 2$ .

Factor $16$ out of $32$ .

$x + 7 = \pm \sqrt{16 (2)}$

Rewrite $16$ as $4^{2}$ .

$x + 7 = \pm \sqrt{4^{2} \cdot 2}$

Pull terms out from under the radical.

$x + 7 = \pm 4 \sqrt{2}$

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.

$x + 7 = 4 \sqrt{2}$

Subtract $7$ from both sides of the equation.

$x = 4 \sqrt{2} - 7$

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

$x + 7 = - 4 \sqrt{2}$

Subtract $7$ from both sides of the equation.

$x = - 4 \sqrt{2} - 7$

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

$x = 4 \sqrt{2} - 7, - 4 \sqrt{2} - 7$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 4 \sqrt{2} - 7, - 4 \sqrt{2} - 7$

Decimal Form:

$x = - 1.34314575 \dots, - 12.65685424 \dots$