Solve 4x^2+12=0

$$4 x ^ { 2 } + 12 = 0$$

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

$$4x^{2}=-12$$

Divide both sides by 4.

$$x^{2}=\frac{-12}{4}$$

Divide -12 by 4 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.

$$4x^{2}+12=0$$

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

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

Square 0.

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

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\times 12}}{2\times 4}$$

Multiply -16 times 12.

$$x=\frac{0±\sqrt{-192}}{2\times 4}$$

Take the square root of -192.

$$x=\frac{0±8\sqrt{3}i}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±8\sqrt{3}i}{8}$$

Now solve the equation x=\frac{0±8\sqrt{3}i}{8} when ± is plus.

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

Now solve the equation x=\frac{0±8\sqrt{3}i}{8} when ± is minus.

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

The equation is now solved.

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