Solve 12x^2+48=0

$$12 x ^ { 2 } + 48 = 0$$

Solve for x (complex solution)

$$x=-2i$$

$$x=2i$$

Steps by Finding Square Root

Subtract 48 from both sides. Anything subtracted from zero gives its negation.

$$12x^{2}=-48$$

Divide both sides by 12.

$$x^{2}=\frac{-48}{12}$$

Divide -48 by 12 to get -4.

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

The equation is now solved.

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

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.

$$12x^{2}+48=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 12 for a, 0 for b, and 48 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 12\times 48}}{2\times 12}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 12\times 48}}{2\times 12}$$

Multiply -4 times 12.

$$x=\frac{0±\sqrt{-48\times 48}}{2\times 12}$$

Multiply -48 times 48.

$$x=\frac{0±\sqrt{-2304}}{2\times 12}$$

Take the square root of -2304.

$$x=\frac{0±48i}{2\times 12}$$

Multiply 2 times 12.

$$x=\frac{0±48i}{24}$$

Now solve the equation x=\frac{0±48i}{24} when ± is plus.

$$x=2i$$

Now solve the equation x=\frac{0±48i}{24} when ± is minus.

$$x=-2i$$

The equation is now solved.

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