Solve 3x^2+8=0

$$3 { x }^{ 2 } +8=0$$

Solve for x (complex solution)

$$x=-\frac{2\sqrt{6}i}{3}\approx -0-1.632993162i$$

$$x=\frac{2\sqrt{6}i}{3}\approx 1.632993162i$$

Steps by Finding Square Root

Subtract 8 from both sides. Anything subtracted from zero gives its negation.

$$3x^{2}=-8$$

Divide both sides by 3.

$$x^{2}=-\frac{8}{3}$$

The equation is now solved.

$$x=\frac{2\sqrt{6}i}{3} x=-\frac{2\sqrt{6}i}{3}$$

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.

$$3x^{2}+8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and 8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\times 8}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\times 8}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\times 8}}{2\times 3}$$

Multiply -12 times 8.

$$x=\frac{0±\sqrt{-96}}{2\times 3}$$

Take the square root of -96.

$$x=\frac{0±4\sqrt{6}i}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±4\sqrt{6}i}{6}$$

Now solve the equation x=\frac{0±4\sqrt{6}i}{6} when ± is plus.

$$x=\frac{2\sqrt{6}i}{3}$$

Now solve the equation x=\frac{0±4\sqrt{6}i}{6} when ± is minus.

$$x=-\frac{2\sqrt{6}i}{3}$$

The equation is now solved.

$$x=\frac{2\sqrt{6}i}{3} x=-\frac{2\sqrt{6}i}{3}$$