Solve 3(x^2-2)+18=0

$$3 ( x ^ { 2 } - 2 ) + 18 = 0$$

Solve for x (complex solution)

$$x=-2i$$

$$x=2i$$

Steps by Finding Square Root

Use the distributive property to multiply 3 by x^{2}-2.

$$3x^{2}-6+18=0$$

Add -6 and 18 to get 12.

$$3x^{2}+12=0$$

Subtract 12 from both sides. Anything subtracted from zero gives its negation.

$$3x^{2}=-12$$

Divide both sides by 3.

$$x^{2}=\frac{-12}{3}$$

Divide -12 by 3 to get -4.

$$x^{2}=-4$$

The equation is now solved.

$$x=2i x=-2i$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 3 by x^{2}-2.

$$3x^{2}-6+18=0$$

Add -6 and 18 to get 12.

$$3x^{2}+12=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and 12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\times 12}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\times 12}}{2\times 3}$$

Multiply -4 times 3.

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

Multiply -12 times 12.

$$x=\frac{0±\sqrt{-144}}{2\times 3}$$

Take the square root of -144.

$$x=\frac{0±12i}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±12i}{6}$$

Now solve the equation x=\frac{0±12i}{6} when ± is plus.

$$x=2i$$

Now solve the equation x=\frac{0±12i}{6} when ± is minus.

$$x=-2i$$

The equation is now solved.

$$x=2i x=-2i$$