Solve Using the Square Root Property 2/3x^2-6=0

$\frac{2}{3} x^{2} - 6 = 0$

Step 1

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

$\frac{2 x^{2}}{3} - 6 = 0$

Step 2

Add $6$ to both sides of the equation.

$\frac{2 x^{2}}{3} = 6$

Step 3

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} \cdot \frac{2 x^{2}}{3} = \frac{3}{2} \cdot 6$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{2} \cdot \frac{2 x^{2}}{3}$ .

Combine.

$\frac{3 (2 x^{2})}{2 \cdot 3} = \frac{3}{2} \cdot 6$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 (2 x^{2})}{2 \cdot 3} = \frac{3}{2} \cdot 6$

Rewrite the expression.

$\frac{2 x^{2}}{2} = \frac{3}{2} \cdot 6$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{3}{2} \cdot 6$

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

$x^{2} = \frac{3}{2} \cdot 6$

Simplify the right side.

Simplify $\frac{3}{2} \cdot 6$ .

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $3$ by $3$ .

$x^{2} = 9$

Step 5

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

$x = \pm \sqrt{9}$

Step 6

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 7

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.

$x = 3, - 3$

Solve Using the Square Root Property 2/3x^2-6=0

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