Solve Using the Square Root Property (x+3)^2=11

${(x + 3)}^{2} = 11$

Step 1

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

$x + 3 = \pm \sqrt{11}$

Step 2

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.

$x + 3 = \sqrt{11}$

Subtract $3$ from both sides of the equation.

$x = \sqrt{11} - 3$

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

$x + 3 = - \sqrt{11}$

Subtract $3$ from both sides of the equation.

$x = - \sqrt{11} - 3$

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

$x = \sqrt{11} - 3, - \sqrt{11} - 3$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{11} - 3, - \sqrt{11} - 3$

Decimal Form:

$x = 0.31662479 \dots, - 6.31662479 \dots$