Solve x^2+sqrt{1/6}=0

$$x ^ { 2 } + \sqrt { \frac { 1 } { 6 } } = 0$$

Solve for x (complex solution)

$$x=-\frac{6^{\frac{3}{4}}i}{6}\approx -0-0.638943104i$$

$$x=\frac{6^{\frac{3}{4}}i}{6}\approx 0.638943104i$$

Steps by Finding Square Root

Rewrite the square root of the division \sqrt{\frac{1}{6}} as the division of square roots \frac{\sqrt{1}}{\sqrt{6}}.

$$x^{2}+\frac{\sqrt{1}}{\sqrt{6}}=0$$

Calculate the square root of 1 and get 1.

$$x^{2}+\frac{1}{\sqrt{6}}=0$$

Rationalize the denominator of \frac{1}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$x^{2}+\frac{\sqrt{6}}{\left(\sqrt{6}\right)^{2}}=0$$

The square of \sqrt{6} is 6.

$$x^{2}+\frac{\sqrt{6}}{6}=0$$

Subtract \frac{\sqrt{6}}{6} from both sides. Anything subtracted from zero gives its negation.

$$x^{2}=-\frac{\sqrt{6}}{6}$$

Take the square root of both sides of the equation.

$$x=\frac{6^{\frac{3}{4}}i}{6} x=-\frac{6^{\frac{3}{4}}i}{6}$$

Steps Using the Quadratic Formula

Rewrite the square root of the division \sqrt{\frac{1}{6}} as the division of square roots \frac{\sqrt{1}}{\sqrt{6}}.

$$x^{2}+\frac{\sqrt{1}}{\sqrt{6}}=0$$

Calculate the square root of 1 and get 1.

$$x^{2}+\frac{1}{\sqrt{6}}=0$$

Rationalize the denominator of \frac{1}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$x^{2}+\frac{\sqrt{6}}{\left(\sqrt{6}\right)^{2}}=0$$

The square of \sqrt{6} is 6.

$$x^{2}+\frac{\sqrt{6}}{6}=0$$

Multiply both sides of the equation by 6.

$$6x^{2}+\sqrt{6}=0$$

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

$$x=\frac{0±\sqrt{0^{2}-4\times 6\sqrt{6}}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\sqrt{6}}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\sqrt{6}}}{2\times 6}$$

Take the square root of -24\sqrt{6}.

$$x=\frac{0±2\times 6^{\frac{3}{4}}i}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±2\times 6^{\frac{3}{4}}i}{12}$$

Now solve the equation x=\frac{0±2\times 6^{\frac{3}{4}}i}{12} when ± is plus.

$$x=\frac{6^{\frac{3}{4}}i}{6}$$

Now solve the equation x=\frac{0±2\times 6^{\frac{3}{4}}i}{12} when ± is minus.

$$x=-\frac{6^{\frac{3}{4}}i}{6}$$

The equation is now solved.

$$x=\frac{6^{\frac{3}{4}}i}{6} x=-\frac{6^{\frac{3}{4}}i}{6}$$