Solve 3x^2+9=0

$$3 { x }^{ 2 } +9=0$$

Solve for x (complex solution)

$$x=-\sqrt{3}i\approx -0-1.732050808i$$

$$x=\sqrt{3}i\approx 1.732050808i$$

Steps by Finding Square Root

Subtract 9 from both sides. Anything subtracted from zero gives its negation.

$$3x^{2}=-9$$

Divide both sides by 3.

$$x^{2}=\frac{-9}{3}$$

Divide -9 by 3 to get -3.

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

The equation is now solved.

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

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.

$$3x^{2}+9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and 9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\times 9}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\times 9}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\times 9}}{2\times 3}$$

Multiply -12 times 9.

$$x=\frac{0±\sqrt{-108}}{2\times 3}$$

Take the square root of -108.

$$x=\frac{0±6\sqrt{3}i}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±6\sqrt{3}i}{6}$$

Now solve the equation x=\frac{0±6\sqrt{3}i}{6} when ± is plus.

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

Now solve the equation x=\frac{0±6\sqrt{3}i}{6} when ± is minus.

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

The equation is now solved.

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