Solve Using the Square Root Property (x+7)^2=539

${(x + 7)}^{2} = 539$

Step 1

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

$x + 7 = \pm \sqrt{539}$

Step 2

Simplify $\pm \sqrt{539}$ .

Rewrite $539$ as $7^{2} \cdot 11$ .

Factor $49$ out of $539$ .

$x + 7 = \pm \sqrt{49 (11)}$

Rewrite $49$ as $7^{2}$ .

$x + 7 = \pm \sqrt{7^{2} \cdot 11}$

Pull terms out from under the radical.

$x + 7 = \pm 7 \sqrt{11}$

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.

$x + 7 = 7 \sqrt{11}$

Subtract $7$ from both sides of the equation.

$x = 7 \sqrt{11} - 7$

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

$x + 7 = - 7 \sqrt{11}$

Subtract $7$ from both sides of the equation.

$x = - 7 \sqrt{11} - 7$

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

$x = 7 \sqrt{11} - 7, - 7 \sqrt{11} - 7$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = 7 \sqrt{11} - 7, - 7 \sqrt{11} - 7$

Decimal Form:

$x = 16.21637353 \dots, - 30.21637353 \dots$