Solve for x 0=1/3x^2-3

$0 = \frac{1}{3} x^{2} - 3$

Step 1

Rewrite the equation as $\frac{1}{3} x^{2} - 3 = 0$ .

$\frac{1}{3} x^{2} - 3 = 0$

Step 2

Combine $\frac{1}{3}$ and $x^{2}$ .

$\frac{x^{2}}{3} - 3 = 0$

Step 3

Add $3$ to both sides of the equation.

$\frac{x^{2}}{3} = 3$

Step 4

Multiply both sides of the equation by $3$ .

$3 \frac{x^{2}}{3} = 3 \cdot 3$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{x^{2}}{3} = 3 \cdot 3$

Rewrite the expression.

$x^{2} = 3 \cdot 3$

Simplify the right side.

Multiply $3$ by $3$ .

$x^{2} = 9$

Step 6

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

$x = \pm \sqrt{9}$

Step 7

Simplify $\pm \sqrt{9}$ .

Rewrite $9$ as $3^{2}$ .

$x = \pm \sqrt{3^{2}}$

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

$x = \pm 3$

Step 8

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.

$x = 3$

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

$x = - 3$

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

$x = 3, - 3$