Solve 200/1=981/200t^2

$$\frac { 200 } { 1 } = \frac { 981 } { 200 } t ^ { 2 }$$

Solve for t

$$t = \frac{200 \sqrt{109}}{327} \approx 6.385508568$$

$$t = -\frac{200 \sqrt{109}}{327} \approx -6.385508568$$

Steps by Finding Square Root

Anything divided by one gives itself.

$$200=\frac{981}{200}t^{2}$$

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

$$\frac{981}{200}t^{2}=200$$

Multiply both sides by \frac{200}{981}, the reciprocal of \frac{981}{200}.

$$t^{2}=200\times \frac{200}{981}$$

Multiply 200 and \frac{200}{981} to get \frac{40000}{981}.

$$t^{2}=\frac{40000}{981}$$

Take the square root of both sides of the equation.

$$t=\frac{200\sqrt{109}}{327} t=-\frac{200\sqrt{109}}{327}$$

Steps Using the Quadratic Formula

Anything divided by one gives itself.

$$200=\frac{981}{200}t^{2}$$

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

$$\frac{981}{200}t^{2}=200$$

Subtract 200 from both sides.

$$\frac{981}{200}t^{2}-200=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{981}{200} for a, 0 for b, and -200 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\times \frac{981}{200}\left(-200\right)}}{2\times \frac{981}{200}}$$

Square 0.

$$t=\frac{0±\sqrt{-4\times \frac{981}{200}\left(-200\right)}}{2\times \frac{981}{200}}$$

Multiply -4 times \frac{981}{200}.

$$t=\frac{0±\sqrt{-\frac{981}{50}\left(-200\right)}}{2\times \frac{981}{200}}$$

Multiply -\frac{981}{50} times -200.

$$t=\frac{0±\sqrt{3924}}{2\times \frac{981}{200}}$$

Take the square root of 3924.

$$t=\frac{0±6\sqrt{109}}{2\times \frac{981}{200}}$$

Multiply 2 times \frac{981}{200}.

$$t=\frac{0±6\sqrt{109}}{\frac{981}{100}}$$

Now solve the equation t=\frac{0±6\sqrt{109}}{\frac{981}{100}} when ± is plus.

$$t=\frac{200\sqrt{109}}{327}$$

Now solve the equation t=\frac{0±6\sqrt{109}}{\frac{981}{100}} when ± is minus.

$$t=-\frac{200\sqrt{109}}{327}$$

The equation is now solved.

$$t=\frac{200\sqrt{109}}{327} t=-\frac{200\sqrt{109}}{327}$$