Solve for x 23=x^2+7

$23 = x^{2} + 7$

Step 1

Rewrite the equation as $x^{2} + 7 = 23$ .

$x^{2} + 7 = 23$

Step 2

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

Subtract $7$ from both sides of the equation.

$x^{2} = 23 - 7$

Subtract $7$ from $23$ .

$x^{2} = 16$

Step 3

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

$x = \pm \sqrt{16}$

Step 4

Simplify $\pm \sqrt{16}$ .

Rewrite $16$ as $4^{2}$ .

$x = \pm \sqrt{4^{2}}$

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

$x = \pm 4$

Step 5

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.

$x = 4$

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

$x = - 4$

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

$x = 4, - 4$