Solve 2x^2=1/6

$$2 x ^ { 2 } = \frac { 1 } { 6 }$$

Solve for x

$$x=\frac{\sqrt{3}}{6}\approx 0.288675135$$

$$x=-\frac{\sqrt{3}}{6}\approx -0.288675135$$

Steps by Finding Square Root

Divide both sides by 2.

$$x^{2}=\frac{\frac{1}{6}}{2}$$

Express \frac{\frac{1}{6}}{2} as a single fraction.

$$x^{2}=\frac{1}{6\times 2}$$

Multiply 6 and 2 to get 12.

$$x^{2}=\frac{1}{12}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{3}}{6} x=-\frac{\sqrt{3}}{6}$$

Steps Using the Quadratic Formula

Divide both sides by 2.

$$x^{2}=\frac{\frac{1}{6}}{2}$$

Express \frac{\frac{1}{6}}{2} as a single fraction.

$$x^{2}=\frac{1}{6\times 2}$$

Multiply 6 and 2 to get 12.

$$x^{2}=\frac{1}{12}$$

Subtract \frac{1}{12} from both sides.

$$x^{2}-\frac{1}{12}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{1}{12} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{12}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{1}{12}\right)}}{2}$$

Multiply -4 times -\frac{1}{12}.

$$x=\frac{0±\sqrt{\frac{1}{3}}}{2}$$

Take the square root of \frac{1}{3}.

$$x=\frac{0±\frac{\sqrt{3}}{3}}{2}$$

Now solve the equation x=\frac{0±\frac{\sqrt{3}}{3}}{2} when ± is plus.

$$x=\frac{\sqrt{3}}{6}$$

Now solve the equation x=\frac{0±\frac{\sqrt{3}}{3}}{2} when ± is minus.

$$x=-\frac{\sqrt{3}}{6}$$

The equation is now solved.

$$x=\frac{\sqrt{3}}{6} x=-\frac{\sqrt{3}}{6}$$