Solve 12x^2+300=0

$$12 x ^ { 2 } + 300 = 0$$

Solve for x (complex solution)

$$x=-5i$$

$$x=5i$$

Steps by Finding Square Root

Subtract 300 from both sides. Anything subtracted from zero gives its negation.

$$12x^{2}=-300$$

Divide both sides by 12.

$$x^{2}=\frac{-300}{12}$$

Divide -300 by 12 to get -25.

$$x^{2}=-25$$

The equation is now solved.

$$x=5i x=-5i$$

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.

$$12x^{2}+300=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 12 for a, 0 for b, and 300 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 12\times 300}}{2\times 12}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 12\times 300}}{2\times 12}$$

Multiply -4 times 12.

$$x=\frac{0±\sqrt{-48\times 300}}{2\times 12}$$

Multiply -48 times 300.

$$x=\frac{0±\sqrt{-14400}}{2\times 12}$$

Take the square root of -14400.

$$x=\frac{0±120i}{2\times 12}$$

Multiply 2 times 12.

$$x=\frac{0±120i}{24}$$

Now solve the equation x=\frac{0±120i}{24} when ± is plus.

$$x=5i$$

Now solve the equation x=\frac{0±120i}{24} when ± is minus.

$$x=-5i$$

The equation is now solved.

$$x=5i x=-5i$$