Solve Using the Square Root Property 2x^2-432=0

$2 x^{2} - 432 = 0$

Step 1

Add $432$ to both sides of the equation.

$2 x^{2} = 432$

Step 2

Divide each term in $2 x^{2} = 432$ by $2$ and simplify.

Divide each term in $2 x^{2} = 432$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{432}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{432}{2}$

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

$x^{2} = \frac{432}{2}$

Simplify the right side.

Divide $432$ by $2$ .

$x^{2} = 216$

Step 3

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

$x = \pm \sqrt{216}$

Step 4

Simplify $\pm \sqrt{216}$ .

Rewrite $216$ as $6^{2} \cdot 6$ .

Factor $36$ out of $216$ .

$x = \pm \sqrt{36 (6)}$

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

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

Pull terms out from under the radical.

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

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.

$x = 6 \sqrt{6}$

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

$x = - 6 \sqrt{6}$

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

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 14.69693845 \dots, - 14.69693845 \dots$