Solve (1/2)200t^2=10.000

$$( 1 / 2 ) 200 t ^ { 2 } = 10.000$$

Solve for t

$$t=\frac{\sqrt{10}}{10}\approx 0.316227766$$

$$t=-\frac{\sqrt{10}}{10}\approx -0.316227766$$

Steps by Finding Square Root

Multiply \frac{1}{2} and 200 to get 100.

$$100t^{2}=10$$

Divide both sides by 100.

$$t^{2}=\frac{10}{100}$$

Reduce the fraction \frac{10}{100} to lowest terms by extracting and canceling out 10.

$$t^{2}=\frac{1}{10}$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Multiply \frac{1}{2} and 200 to get 100.

$$100t^{2}=10$$

Subtract 10 from both sides.

$$100t^{2}-10=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 100 for a, 0 for b, and -10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\times 100\left(-10\right)}}{2\times 100}$$

Square 0.

$$t=\frac{0±\sqrt{-4\times 100\left(-10\right)}}{2\times 100}$$

Multiply -4 times 100.

$$t=\frac{0±\sqrt{-400\left(-10\right)}}{2\times 100}$$

Multiply -400 times -10.

$$t=\frac{0±\sqrt{4000}}{2\times 100}$$

Take the square root of 4000.

$$t=\frac{0±20\sqrt{10}}{2\times 100}$$

Multiply 2 times 100.

$$t=\frac{0±20\sqrt{10}}{200}$$

Now solve the equation t=\frac{0±20\sqrt{10}}{200} when ± is plus.

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

Now solve the equation t=\frac{0±20\sqrt{10}}{200} when ± is minus.

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

The equation is now solved.

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