How do you solve the equation 2/3x^2-4=12?

Jun 12, 2017

The answer is $x = \pm 2 \sqrt{6}$.
.

Explanation:

Solve:

$\frac{2}{3} {x}^{2} - 4 = 12$

Add $4$ to both sides.

$\frac{2}{3} {x}^{2} - \textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} + \textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} = 12 + 4$

Simplify.

$\frac{2}{3} {x}^{2} = 16$

Multiply both sides by $3$.

$\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} \times \frac{2}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} {x}^{2} = 16 \times 3$

Simplify.

$2 {x}^{2} = 48$

Divide both sides by $2$.

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}} {x}^{2} = \frac{48}{2}$

Simplify.

${x}^{2} = 24$

Take the square root of both sides.

$\sqrt{{x}^{2}} = \pm \sqrt{24}$

Simplify.

$x = \pm \sqrt{24}$

Simplify $\sqrt{24}$ using prime factorization.

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

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

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