Solve Using the Square Root Property (x+2)^2=68

${(x + 2)}^{2} = 68$

Step 1

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

$x + 2 = \pm \sqrt{68}$

Step 2

Simplify $\pm \sqrt{68}$ .

Rewrite $68$ as $2^{2} \cdot 17$ .

Factor $4$ out of $68$ .

$x + 2 = \pm \sqrt{4 (17)}$

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

$x + 2 = \pm \sqrt{2^{2} \cdot 17}$

Pull terms out from under the radical.

$x + 2 = \pm 2 \sqrt{17}$

Step 3

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.

$x + 2 = 2 \sqrt{17}$

Subtract $2$ from both sides of the equation.

$x = 2 \sqrt{17} - 2$

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

$x + 2 = - 2 \sqrt{17}$

Subtract $2$ from both sides of the equation.

$x = - 2 \sqrt{17} - 2$

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

$x = 2 \sqrt{17} - 2, - 2 \sqrt{17} - 2$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = 2 \sqrt{17} - 2, - 2 \sqrt{17} - 2$

Decimal Form:

$x = 6.24621125 \dots, - 10.24621125 \dots$