Solve 2=5t^2

$$2 = 5 t ^ { 2 }$$

Solve for t

$$t=\frac{\sqrt{10}}{5}\approx 0.632455532$$

$$t=-\frac{\sqrt{10}}{5}\approx -0.632455532$$

Steps by Finding Square Root

Divide both sides by 5.

$$\frac{2}{5}=t^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$t^{2}=\frac{2}{5}$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Divide both sides by 5.

$$\frac{2}{5}=t^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$t^{2}=\frac{2}{5}$$

Subtract \frac{2}{5} from both sides.

$$t^{2}-\frac{2}{5}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{2}{5} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\left(-\frac{2}{5}\right)}}{2}$$

Square 0.

$$t=\frac{0±\sqrt{-4\left(-\frac{2}{5}\right)}}{2}$$

Multiply -4 times -\frac{2}{5}.

$$t=\frac{0±\sqrt{\frac{8}{5}}}{2}$$

Take the square root of \frac{8}{5}.

$$t=\frac{0±\frac{2\sqrt{10}}{5}}{2}$$

Now solve the equation t=\frac{0±\frac{2\sqrt{10}}{5}}{2} when ± is plus.

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

Now solve the equation t=\frac{0±\frac{2\sqrt{10}}{5}}{2} when ± is minus.

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

The equation is now solved.

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