Solve (1/2)200t^2=10,000

$$( 1 / 2 ) 200 t ^ { 2 } = 10,000$$

Solve for t

$$t=10$$

$$t=-10$$

Steps Using Difference of Squares

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

$$100t^{2}=10000$$

Subtract 10000 from both sides.

$$100t^{2}-10000=0$$

Divide both sides by 100.

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

Consider t^{2}-100. Rewrite t^{2}-100 as t^{2}-10^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(t-10\right)\left(t+10\right)=0$$

To find equation solutions, solve t-10=0 and t+10=0.

$$t=10 t=-10$$

Steps by Finding Square Root

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

$$100t^{2}=10000$$

Divide both sides by 100.

$$t^{2}=\frac{10000}{100}$$

Divide 10000 by 100 to get 100.

$$t^{2}=100$$

Take the square root of both sides of the equation.

$$t=10 t=-10$$

Steps Using the Quadratic Formula

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

$$100t^{2}=10000$$

Subtract 10000 from both sides.

$$100t^{2}-10000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 100 for a, 0 for b, and -10000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\times 100\left(-10000\right)}}{2\times 100}$$

Square 0.

$$t=\frac{0±\sqrt{-4\times 100\left(-10000\right)}}{2\times 100}$$

Multiply -4 times 100.

$$t=\frac{0±\sqrt{-400\left(-10000\right)}}{2\times 100}$$

Multiply -400 times -10000.

$$t=\frac{0±\sqrt{4000000}}{2\times 100}$$

Take the square root of 4000000.

$$t=\frac{0±2000}{2\times 100}$$

Multiply 2 times 100.

$$t=\frac{0±2000}{200}$$

Now solve the equation t=\frac{0±2000}{200} when ± is plus. Divide 2000 by 200.

$$t=10$$

Now solve the equation t=\frac{0±2000}{200} when ± is minus. Divide -2000 by 200.

$$t=-10$$

The equation is now solved.

$$t=10 t=-10$$