Solve 3x^2+8=2

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

Solve for x (complex solution)

$$x=-\sqrt{2}i\approx -0-1.414213562i$$

$$x=\sqrt{2}i\approx 1.414213562i$$

Steps by Finding Square Root

Subtract 8 from both sides.

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

Subtract 8 from 2 to get -6.

$$3x^{2}=-6$$

Divide both sides by 3.

$$x^{2}=\frac{-6}{3}$$

Divide -6 by 3 to get -2.

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

The equation is now solved.

$$x=\sqrt{2}i x=-\sqrt{2}i$$

Steps Using the Quadratic Formula

Subtract 2 from both sides.

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

Subtract 2 from 8 to get 6.

$$3x^{2}+6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and 6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\times 6}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\times 6}}{2\times 3}$$

Multiply -12 times 6.

$$x=\frac{0±\sqrt{-72}}{2\times 3}$$

Take the square root of -72.

$$x=\frac{0±6\sqrt{2}i}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±6\sqrt{2}i}{6}$$

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

$$x=\sqrt{2}i$$

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

$$x=-\sqrt{2}i$$

The equation is now solved.

$$x=\sqrt{2}i x=-\sqrt{2}i$$