Solve -24x^2-8=0

$$- 24 x ^ { 2 } - 8 = 0$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{3}i}{3}\approx -0-0.577350269i$$

$$x=\frac{\sqrt{3}i}{3}\approx 0.577350269i$$

Steps by Finding Square Root

Add 8 to both sides. Anything plus zero gives itself.

$$-24x^{2}=8$$

Divide both sides by -24.

$$x^{2}=\frac{8}{-24}$$

Reduce the fraction \frac{8}{-24} to lowest terms by extracting and canceling out 8.

$$x^{2}=-\frac{1}{3}$$

The equation is now solved.

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

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.

$$-24x^{2}-8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -24 for a, 0 for b, and -8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-24\right)\left(-8\right)}}{2\left(-24\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-24\right)\left(-8\right)}}{2\left(-24\right)}$$

Multiply -4 times -24.

$$x=\frac{0±\sqrt{96\left(-8\right)}}{2\left(-24\right)}$$

Multiply 96 times -8.

$$x=\frac{0±\sqrt{-768}}{2\left(-24\right)}$$

Take the square root of -768.

$$x=\frac{0±16\sqrt{3}i}{2\left(-24\right)}$$

Multiply 2 times -24.

$$x=\frac{0±16\sqrt{3}i}{-48}$$

Now solve the equation x=\frac{0±16\sqrt{3}i}{-48} when ± is plus.

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

Now solve the equation x=\frac{0±16\sqrt{3}i}{-48} when ± is minus.

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

The equation is now solved.

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