Solve for x 0=2x^2-6

$0 = 2 x^{2} - 6$

Step 1

Rewrite the equation as $2 x^{2} - 6 = 0$ .

$2 x^{2} - 6 = 0$

Step 2

Add $6$ to both sides of the equation.

$2 x^{2} = 6$

Step 3

Divide each term in $2 x^{2} = 6$ by $2$ and simplify.

Divide each term in $2 x^{2} = 6$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{6}{2}$

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

$x^{2} = \frac{6}{2}$

Simplify the right side.

Divide $6$ by $2$ .

$x^{2} = 3$

Step 4

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

$x = \pm \sqrt{3}$

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.

$x = \sqrt{3}$

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

$x = - \sqrt{3}$

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

$x = \sqrt{3}, - \sqrt{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{3}, - \sqrt{3}$

Decimal Form:

$x = 1.73205080 \dots, - 1.73205080 \dots$