Solve 6x^2+108=0

$$6 { x }^{ 2 } +108=0$$

Solve for x (complex solution)

$$x=-3\sqrt{2}i\approx -0-4.242640687i$$

$$x=3\sqrt{2}i\approx 4.242640687i$$

Steps by Finding Square Root

Subtract 108 from both sides. Anything subtracted from zero gives its negation.

$$6x^{2}=-108$$

Divide both sides by 6.

$$x^{2}=\frac{-108}{6}$$

Divide -108 by 6 to get -18.

$$x^{2}=-18$$

The equation is now solved.

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

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.

$$6x^{2}+108=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and 108 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\times 108}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\times 108}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\times 108}}{2\times 6}$$

Multiply -24 times 108.

$$x=\frac{0±\sqrt{-2592}}{2\times 6}$$

Take the square root of -2592.

$$x=\frac{0±36\sqrt{2}i}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±36\sqrt{2}i}{12}$$

Now solve the equation x=\frac{0±36\sqrt{2}i}{12} when ± is plus.

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

Now solve the equation x=\frac{0±36\sqrt{2}i}{12} when ± is minus.

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

The equation is now solved.

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