Solve Using the Square Root Property 2x^2-72=0

$2 x^{2} - 72 = 0$

Step 1

Add $72$ to both sides of the equation.

$2 x^{2} = 72$

Step 2

Divide each term in $2 x^{2} = 72$ by $2$ and simplify.

Divide each term in $2 x^{2} = 72$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{72}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{72}{2}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{72}{2}$

Simplify the right side.

Divide $72$ by $2$ .

$x^{2} = 36$

Step 3

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

$x = \pm \sqrt{36}$

Step 4

Simplify $\pm \sqrt{36}$ .

Rewrite $36$ as $6^{2}$ .

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

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

$x = \pm 6$

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.

$x = 6$

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

$x = - 6$

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

$x = 6, - 6$