Solve Using the Square Root Property 2(x+1)^2=24

$2 {(x + 1)}^{2} = 24$

Step 1

Divide each term in $2 {(x + 1)}^{2} = 24$ by $2$ and simplify.

Divide each term in $2 {(x + 1)}^{2} = 24$ by $2$ .

$\frac{2 {(x + 1)}^{2}}{2} = \frac{24}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 {(x + 1)}^{2}}{2} = \frac{24}{2}$

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

${(x + 1)}^{2} = \frac{24}{2}$

Simplify the right side.

Divide $24$ by $2$ .

${(x + 1)}^{2} = 12$

Step 2

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

$x + 1 = \pm \sqrt{12}$

Step 3

Simplify $\pm \sqrt{12}$ .

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$x + 1 = \pm \sqrt{4 (3)}$

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

$x + 1 = \pm \sqrt{2^{2} \cdot 3}$

Pull terms out from under the radical.

$x + 1 = \pm 2 \sqrt{3}$

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.

$x + 1 = 2 \sqrt{3}$

Subtract $1$ from both sides of the equation.

$x = 2 \sqrt{3} - 1$

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

$x + 1 = - 2 \sqrt{3}$

Subtract $1$ from both sides of the equation.

$x = - 2 \sqrt{3} - 1$

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

$x = 2 \sqrt{3} - 1, - 2 \sqrt{3} - 1$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 2 \sqrt{3} - 1, - 2 \sqrt{3} - 1$

Decimal Form:

$x = 2.46410161 \dots, - 4.46410161 \dots$