Solve Using the Square Root Property x^2+6=31

$x^{2} + 6 = 31$

Step 1

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

Subtract $6$ from both sides of the equation.

$x^{2} = 31 - 6$

Subtract $6$ from $31$ .

$x^{2} = 25$

Step 2

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

$x = \pm \sqrt{25}$

Step 3

Simplify $\pm \sqrt{25}$ .

Rewrite $25$ as $5^{2}$ .

$x = \pm \sqrt{5^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 5$

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.

$x = 5$

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

$x = - 5$

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

$x = 5, - 5$