Solve t^2=-1/30-1/60

$$t ^ { 2 } = - \frac { 1 } { 30 } - \frac { 1 } { 60 }$$

Solve for t

$$t=-\frac{\sqrt{5}i}{10}\approx -0-0.223606798i$$

$$t=\frac{\sqrt{5}i}{10}\approx 0.223606798i$$

Steps by Finding Square Root

Subtract \frac{1}{60} from -\frac{1}{30} to get -\frac{1}{20}.

$$t^{2}=-\frac{1}{20}$$

The equation is now solved.

$$t=\frac{\sqrt{5}i}{10} t=-\frac{\sqrt{5}i}{10}$$

Steps Using the Quadratic Formula

Subtract \frac{1}{60} from -\frac{1}{30} to get -\frac{1}{20}.

$$t^{2}=-\frac{1}{20}$$

Add \frac{1}{20} to both sides.

$$t^{2}+\frac{1}{20}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and \frac{1}{20} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\times \frac{1}{20}}}{2}$$

Square 0.

$$t=\frac{0±\sqrt{-4\times \frac{1}{20}}}{2}$$

Multiply -4 times \frac{1}{20}.

$$t=\frac{0±\sqrt{-\frac{1}{5}}}{2}$$

Take the square root of -\frac{1}{5}.

$$t=\frac{0±\frac{\sqrt{5}i}{5}}{2}$$

Now solve the equation t=\frac{0±\frac{\sqrt{5}i}{5}}{2} when ± is plus.

$$t=\frac{\sqrt{5}i}{10}$$

Now solve the equation t=\frac{0±\frac{\sqrt{5}i}{5}}{2} when ± is minus.

$$t=-\frac{\sqrt{5}i}{10}$$

The equation is now solved.

$$t=\frac{\sqrt{5}i}{10} t=-\frac{\sqrt{5}i}{10}$$