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

$x^{2} + 5 = 11$

Step 1

Move all terms not containing $x$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

$x^{2} = 11 - 5$

Subtract $5$ from $11$ .

$x^{2} = 6$

Step 2

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

$x = \pm \sqrt{6}$

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.

$x = \sqrt{6}$

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

$x = - \sqrt{6}$

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

$x = \sqrt{6}, - \sqrt{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{6}, - \sqrt{6}$

Decimal Form:

$x = 2.44948974 \dots, - 2.44948974 \dots$