Solve Using the Quadratic Formula 0=1/3x^2-3

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

Step 1

Move all terms to the left side of the equation and simplify.

Simplify the right side.

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

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

Move all the expressions to the left side of the equation.

Subtract $\frac{x^{2}}{3}$ from both sides of the equation.

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

Add $3$ to both sides of the equation.

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

Step 2

Multiply through by the least common denominator $3$ , then simplify.

Apply the distributive property.

$3 (- \frac{x^{2}}{3}) + 3 \cdot 3 = 0$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{x^{2}}{3}$ into the numerator.

$3 (\frac{- x^{2}}{3}) + 3 \cdot 3 = 0$

Cancel the common factor.

$3 (\frac{- x^{2}}{3}) + 3 \cdot 3 = 0$

Rewrite the expression.

$- x^{2} + 3 \cdot 3 = 0$

Multiply $3$ by $3$ .

$- x^{2} + 9 = 0$

Step 3

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 4

Substitute the values $a = - 1$ , $b = 0$ , and $c = 9$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (- 1 \cdot 9)}}{2 \cdot - 1}$

Step 5

Simplify.

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 1 \cdot 9}}{2 \cdot - 1}$

Multiply $- 4 \cdot - 1 \cdot 9$ .

Multiply $- 4$ by $- 1$ .

$x = \frac{0 \pm \sqrt{0 + 4 \cdot 9}}{2 \cdot - 1}$

Multiply $4$ by $9$ .

$x = \frac{0 \pm \sqrt{0 + 36}}{2 \cdot - 1}$

Add $0$ and $36$ .

$x = \frac{0 \pm \sqrt{36}}{2 \cdot - 1}$

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

$x = \frac{0 \pm \sqrt{6^{2}}}{2 \cdot - 1}$

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

$x = \frac{0 \pm 6}{2 \cdot - 1}$

Multiply $2$ by $- 1$ .

$x = \frac{0 \pm 6}{- 2}$

Simplify $\frac{0 \pm 6}{- 2}$ .

$x = \pm 3$

Step 6

The final answer is the combination of both solutions.

$x = 3, - 3$

Solve Using the Quadratic Formula 0=1/3x^2-3

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