Solve 2/3x^2-7=47

$$\frac{ 2 }{ 3 } { x }^{ 2 } -7=47$$

Solve for x

$$x=9$$

$$x=-9$$

Steps Using Difference of Squares

Subtract 47 from both sides.

$$\frac{2}{3}x^{2}-7-47=0$$

Subtract 47 from -7 to get -54.

$$\frac{2}{3}x^{2}-54=0$$

Divide both sides by \frac{2}{3}.

$$x^{2}-81=0$$

Consider x^{2}-81. Rewrite x^{2}-81 as x^{2}-9^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-9\right)\left(x+9\right)=0$$

To find equation solutions, solve x-9=0 and x+9=0.

$$x=9 x=-9$$

Steps by Finding Square Root

Add 7 to both sides.

$$\frac{2}{3}x^{2}=47+7$$

Add 47 and 7 to get 54.

$$\frac{2}{3}x^{2}=54$$

Multiply both sides by \frac{3}{2}, the reciprocal of \frac{2}{3}.

$$x^{2}=54\times \frac{3}{2}$$

Multiply 54 and \frac{3}{2} to get 81.

$$x^{2}=81$$

Take the square root of both sides of the equation.

$$x=9 x=-9$$

Steps Using the Quadratic Formula

Subtract 47 from both sides.

$$\frac{2}{3}x^{2}-7-47=0$$

Subtract 47 from -7 to get -54.

$$\frac{2}{3}x^{2}-54=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{2}{3} for a, 0 for b, and -54 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{2}{3}\left(-54\right)}}{2\times \frac{2}{3}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{2}{3}\left(-54\right)}}{2\times \frac{2}{3}}$$

Multiply -4 times \frac{2}{3}.

$$x=\frac{0±\sqrt{-\frac{8}{3}\left(-54\right)}}{2\times \frac{2}{3}}$$

Multiply -\frac{8}{3} times -54.

$$x=\frac{0±\sqrt{144}}{2\times \frac{2}{3}}$$

Take the square root of 144.

$$x=\frac{0±12}{2\times \frac{2}{3}}$$

Multiply 2 times \frac{2}{3}.

$$x=\frac{0±12}{\frac{4}{3}}$$

Now solve the equation x=\frac{0±12}{\frac{4}{3}} when ± is plus. Divide 12 by \frac{4}{3} by multiplying 12 by the reciprocal of \frac{4}{3}.

$$x=9$$

Now solve the equation x=\frac{0±12}{\frac{4}{3}} when ± is minus. Divide -12 by \frac{4}{3} by multiplying -12 by the reciprocal of \frac{4}{3}.

$$x=-9$$

The equation is now solved.

$$x=9 x=-9$$