Solve 50=9,81t^2/2

$$50 = \frac { 9,81 t ^ { 2 } } { 2 }$$

Solve for t

$$t = \frac{100 \sqrt{109}}{327} \approx 3.192754284$$

$$t = -\frac{100 \sqrt{109}}{327} \approx -3.192754284$$

Steps by Finding Square Root

Multiply both sides by 2.

$$50\times 2=9,81t^{2}$$

Multiply 50 and 2 to get 100.

$$100=9,81t^{2}$$

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

$$9,81t^{2}=100$$

Divide both sides by 9,81.

$$t^{2}=\frac{100}{9,81}$$

Expand \frac{100}{9,81} by multiplying both numerator and the denominator by 100.

$$t^{2}=\frac{10000}{981}$$

Take the square root of both sides of the equation.

$$t=\frac{100\sqrt{109}}{327} t=-\frac{100\sqrt{109}}{327}$$

Steps Using the Quadratic Formula

Multiply both sides by 2.

$$50\times 2=9,81t^{2}$$

Multiply 50 and 2 to get 100.

$$100=9,81t^{2}$$

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

$$9,81t^{2}=100$$

Subtract 100 from both sides.

$$9,81t^{2}-100=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9,81 for a, 0 for b, and -100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\times 9,81\left(-100\right)}}{2\times 9,81}$$

Square 0.

$$t=\frac{0±\sqrt{-4\times 9,81\left(-100\right)}}{2\times 9,81}$$

Multiply -4 times 9,81.

$$t=\frac{0±\sqrt{-39,24\left(-100\right)}}{2\times 9,81}$$

Multiply -39,24 times -100.

$$t=\frac{0±\sqrt{3924}}{2\times 9,81}$$

Take the square root of 3924.

$$t=\frac{0±6\sqrt{109}}{2\times 9,81}$$

Multiply 2 times 9,81.

$$t=\frac{0±6\sqrt{109}}{19,62}$$

Now solve the equation t=\frac{0±6\sqrt{109}}{19,62} when ± is plus.

$$t=\frac{100\sqrt{109}}{327}$$

Now solve the equation t=\frac{0±6\sqrt{109}}{19,62} when ± is minus.

$$t=-\frac{100\sqrt{109}}{327}$$

The equation is now solved.

$$t=\frac{100\sqrt{109}}{327} t=-\frac{100\sqrt{109}}{327}$$