Solve t^2+12=0

$$t ^ { 2 } + 12 = 0$$

Solve for t

$$t=-2\sqrt{3}i\approx -0-3.464101615i$$

$$t=2\sqrt{3}i\approx 3.464101615i$$

Steps by Finding Square Root

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

$$t^{2}=-12$$

The equation is now solved.

$$t=2\sqrt{3}i t=-2\sqrt{3}i$$

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.

$$t^{2}+12=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 0.

$$t=\frac{0±\sqrt{-4\times 12}}{2}$$

Multiply -4 times 12.

$$t=\frac{0±\sqrt{-48}}{2}$$

Take the square root of -48.

$$t=\frac{0±4\sqrt{3}i}{2}$$

Now solve the equation t=\frac{0±4\sqrt{3}i}{2} when ± is plus.

$$t=2\sqrt{3}i$$

Now solve the equation t=\frac{0±4\sqrt{3}i}{2} when ± is minus.

$$t=-2\sqrt{3}i$$

The equation is now solved.

$$t=2\sqrt{3}i t=-2\sqrt{3}i$$