Solve Using the Square Root Property 2(x+2)^2-5=11

$2 {(x + 2)}^{2} - 5 = 11$

Step 1

Add $5$ to both sides of the equation.

$2 {(x + 2)}^{2} = 11 + 5$

Step 2

Add $11$ and $5$ .

$2 {(x + 2)}^{2} = 16$

Step 3

Divide each term in $2 {(x + 2)}^{2} = 16$ by $2$ and simplify.

Divide each term in $2 {(x + 2)}^{2} = 16$ by $2$ .

$\frac{2 {(x + 2)}^{2}}{2} = \frac{16}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 {(x + 2)}^{2}}{2} = \frac{16}{2}$

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

${(x + 2)}^{2} = \frac{16}{2}$

Simplify the right side.

Divide $16$ by $2$ .

${(x + 2)}^{2} = 8$

Step 4

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

$x + 2 = \pm \sqrt{8}$

Step 5

Simplify $\pm \sqrt{8}$ .

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$x + 2 = \pm \sqrt{4 (2)}$

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

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

Pull terms out from under the radical.

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

Step 6

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.

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

Subtract $2$ from both sides of the equation.

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

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

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

Subtract $2$ from both sides of the equation.

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

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

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.82842712 \dots, - 4.82842712 \dots$

Solve Using the Square Root Property 2(x+2)^2-5=11

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