Solve x^2+2+1/3=0

$${ x }^{ 2 } +2+ \frac{ 1 }{ 3 } =0$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{21}i}{3}\approx -0-1.527525232i$$

$$x=\frac{\sqrt{21}i}{3}\approx 1.527525232i$$

Steps by Finding Square Root

Add 2 and \frac{1}{3} to get \frac{7}{3}.

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

Subtract \frac{7}{3} from both sides. Anything subtracted from zero gives its negation.

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

The equation is now solved.

$$x=\frac{\sqrt{21}i}{3} x=-\frac{\sqrt{21}i}{3}$$

Steps Using the Quadratic Formula

Add 2 and \frac{1}{3} to get \frac{7}{3}.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and \frac{7}{3} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{7}{3}}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{7}{3}}}{2}$$

Multiply -4 times \frac{7}{3}.

$$x=\frac{0±\sqrt{-\frac{28}{3}}}{2}$$

Take the square root of -\frac{28}{3}.

$$x=\frac{0±\frac{2\sqrt{21}i}{3}}{2}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{21}i}{3}}{2} when ± is plus.

$$x=\frac{\sqrt{21}i}{3}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{21}i}{3}}{2} when ± is minus.

$$x=-\frac{\sqrt{21}i}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{21}i}{3} x=-\frac{\sqrt{21}i}{3}$$