Solve 3x^2=-21

$$3 x ^ { 2 } = - 21$$

Solve for x (complex solution)

$$x=-\sqrt{7}i\approx -0-2.645751311i$$

$$x=\sqrt{7}i\approx 2.645751311i$$

Steps by Finding Square Root

Divide both sides by 3.

$$x^{2}=\frac{-21}{3}$$

Divide -21 by 3 to get -7.

$$x^{2}=-7$$

The equation is now solved.

$$x=\sqrt{7}i x=-\sqrt{7}i$$

Steps Using the Quadratic Formula

Divide both sides by 3.

$$x^{2}=\frac{-21}{3}$$

Divide -21 by 3 to get -7.

$$x^{2}=-7$$

Add 7 to both sides.

$$x^{2}+7=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 7 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 7}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 7}}{2}$$

Multiply -4 times 7.

$$x=\frac{0±\sqrt{-28}}{2}$$

Take the square root of -28.

$$x=\frac{0±2\sqrt{7}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{7}i}{2} when ± is plus.

$$x=\sqrt{7}i$$

Now solve the equation x=\frac{0±2\sqrt{7}i}{2} when ± is minus.

$$x=-\sqrt{7}i$$

The equation is now solved.

$$x=\sqrt{7}i x=-\sqrt{7}i$$