Solve 1/3(6x^2-4)=11

$$1 / 3 ( 6 x ^ { 2 } - 4 ) = 11$$

Solve for x

$$x = \frac{\sqrt{222}}{6} \approx 2.483277404$$

$$x = -\frac{\sqrt{222}}{6} \approx -2.483277404$$

Steps by Finding Square Root

Multiply both sides by 3, the reciprocal of \frac{1}{3}.

$$6x^{2}-4=11\times 3$$

Multiply 11 and 3 to get 33.

$$6x^{2}-4=33$$

Add 4 to both sides.

$$6x^{2}=33+4$$

Add 33 and 4 to get 37.

$$6x^{2}=37$$

Divide both sides by 6.

$$x^{2}=\frac{37}{6}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{222}}{6} x=-\frac{\sqrt{222}}{6}$$

Steps Using the Quadratic Formula

Multiply both sides by 3, the reciprocal of \frac{1}{3}.

$$6x^{2}-4=11\times 3$$

Multiply 11 and 3 to get 33.

$$6x^{2}-4=33$$

Subtract 33 from both sides.

$$6x^{2}-4-33=0$$

Subtract 33 from -4 to get -37.

$$6x^{2}-37=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and -37 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-37\right)}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\left(-37\right)}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\left(-37\right)}}{2\times 6}$$

Multiply -24 times -37.

$$x=\frac{0±\sqrt{888}}{2\times 6}$$

Take the square root of 888.

$$x=\frac{0±2\sqrt{222}}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±2\sqrt{222}}{12}$$

Now solve the equation x=\frac{0±2\sqrt{222}}{12} when ± is plus.

$$x=\frac{\sqrt{222}}{6}$$

Now solve the equation x=\frac{0±2\sqrt{222}}{12} when ± is minus.

$$x=-\frac{\sqrt{222}}{6}$$

The equation is now solved.

$$x=\frac{\sqrt{222}}{6} x=-\frac{\sqrt{222}}{6}$$