Solve Using the Square Root Property x^2-24=0

$x^{2} - 24 = 0$

Step 1

Add $24$ to both sides of the equation.

$x^{2} = 24$

Step 2

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

$x = \pm \sqrt{24}$

Step 3

Simplify $\pm \sqrt{24}$ .

Rewrite $24$ as $2^{2} \cdot 6$ .

Factor $4$ out of $24$ .

$x = \pm \sqrt{4 (6)}$

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

$x = \pm \sqrt{2^{2} \cdot 6}$

Pull terms out from under the radical.

$x = \pm 2 \sqrt{6}$

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.

$x = 2 \sqrt{6}$

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

$x = - 2 \sqrt{6}$

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

$x = 2 \sqrt{6}, - 2 \sqrt{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 2 \sqrt{6}, - 2 \sqrt{6}$

Decimal Form:

$x = 4.89897948 \dots, - 4.89897948 \dots$