Solve 5t^2=32

$$5 t ^ { 2 } = 32$$

Solve for t

$$t = \frac{4 \sqrt{10}}{5} \approx 2.529822128$$

$$t = -\frac{4 \sqrt{10}}{5} \approx -2.529822128$$

Steps by Finding Square Root

Divide both sides by 5.

$$t^{2}=\frac{32}{5}$$

Take the square root of both sides of the equation.

$$t=\frac{4\sqrt{10}}{5} t=-\frac{4\sqrt{10}}{5}$$

Steps Using the Quadratic Formula

Divide both sides by 5.

$$t^{2}=\frac{32}{5}$$

Subtract \frac{32}{5} from both sides.

$$t^{2}-\frac{32}{5}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{32}{5} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\left(-\frac{32}{5}\right)}}{2}$$

Square 0.

$$t=\frac{0±\sqrt{-4\left(-\frac{32}{5}\right)}}{2}$$

Multiply -4 times -\frac{32}{5}.

$$t=\frac{0±\sqrt{\frac{128}{5}}}{2}$$

Take the square root of \frac{128}{5}.

$$t=\frac{0±\frac{8\sqrt{10}}{5}}{2}$$

Now solve the equation t=\frac{0±\frac{8\sqrt{10}}{5}}{2} when ± is plus.

$$t=\frac{4\sqrt{10}}{5}$$

Now solve the equation t=\frac{0±\frac{8\sqrt{10}}{5}}{2} when ± is minus.

$$t=-\frac{4\sqrt{10}}{5}$$

The equation is now solved.

$$t=\frac{4\sqrt{10}}{5} t=-\frac{4\sqrt{10}}{5}$$