Solve 50(2)=-9.81t^2

$$50 ( 2 ) = - 9.81 t ^ { 2 }$$

Solve for t

$$t=-\frac{i\times 100\sqrt{109}}{327}\approx -0-3.192754284i$$

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

Steps by Finding Square Root

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.

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

Fraction \frac{10000}{-981} can be rewritten as -\frac{10000}{981} by extracting the negative sign.

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

The equation is now solved.

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

Steps Using the Quadratic Formula

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}.

$$t=\frac{0±\sqrt{0^{2}-4\left(-9.81\right)\left(-100\right)}}{2\left(-9.81\right)}$$

Square 0.

$$t=\frac{0±\sqrt{-4\left(-9.81\right)\left(-100\right)}}{2\left(-9.81\right)}$$

Multiply -4 times -9.81.

$$t=\frac{0±\sqrt{39.24\left(-100\right)}}{2\left(-9.81\right)}$$

Multiply 39.24 times -100.

$$t=\frac{0±\sqrt{-3924}}{2\left(-9.81\right)}$$

Take the square root of -3924.

$$t=\frac{0±6\sqrt{109}i}{2\left(-9.81\right)}$$

Multiply 2 times -9.81.

$$t=\frac{0±6\sqrt{109}i}{-19.62}$$

Now solve the equation t=\frac{0±6\sqrt{109}i}{-19.62} when ± is plus.

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

Now solve the equation t=\frac{0±6\sqrt{109}i}{-19.62} when ± is minus.

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

The equation is now solved.

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