Solve -3x^2-2=0

$$- 3 x ^ { 2 } - 2 = 0$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{6}i}{3}\approx -0-0.816496581i$$

$$x=\frac{\sqrt{6}i}{3}\approx 0.816496581i$$

Steps by Finding Square Root

Add 2 to both sides. Anything plus zero gives itself.

$$-3x^{2}=2$$

Divide both sides by -3.

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

The equation is now solved.

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

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-3x^{2}-2=0$$

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

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

Square 0.

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

Multiply -4 times -3.

$$x=\frac{0±\sqrt{12\left(-2\right)}}{2\left(-3\right)}$$

Multiply 12 times -2.

$$x=\frac{0±\sqrt{-24}}{2\left(-3\right)}$$

Take the square root of -24.

$$x=\frac{0±2\sqrt{6}i}{2\left(-3\right)}$$

Multiply 2 times -3.

$$x=\frac{0±2\sqrt{6}i}{-6}$$

Now solve the equation x=\frac{0±2\sqrt{6}i}{-6} when ± is plus.

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

Now solve the equation x=\frac{0±2\sqrt{6}i}{-6} when ± is minus.

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

The equation is now solved.

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