Solve 0=-16t^2+100

$$0 = - 16 t ^ { 2 } + 100$$

Solve for t

$$t = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

$$t = -\frac{5}{2} = -2\frac{1}{2} = -2.5$$

Steps by Finding Square Root

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

$$-16t^{2}+100=0$$

Subtract 100 from both sides. Anything subtracted from zero gives its negation.

$$-16t^{2}=-100$$

Divide both sides by -16.

$$t^{2}=\frac{-100}{-16}$$

Reduce the fraction \frac{-100}{-16} to lowest terms by extracting and canceling out -4.

$$t^{2}=\frac{25}{4}$$

Take the square root of both sides of the equation.

$$t=\frac{5}{2} t=-\frac{5}{2}$$

Steps Using the Quadratic Formula

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

$$-16t^{2}+100=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -16 for a, 0 for b, and 100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\left(-16\right)\times 100}}{2\left(-16\right)}$$

Square 0.

$$t=\frac{0±\sqrt{-4\left(-16\right)\times 100}}{2\left(-16\right)}$$

Multiply -4 times -16.

$$t=\frac{0±\sqrt{64\times 100}}{2\left(-16\right)}$$

Multiply 64 times 100.

$$t=\frac{0±\sqrt{6400}}{2\left(-16\right)}$$

Take the square root of 6400.

$$t=\frac{0±80}{2\left(-16\right)}$$

Multiply 2 times -16.

$$t=\frac{0±80}{-32}$$

Now solve the equation t=\frac{0±80}{-32} when ± is plus. Reduce the fraction \frac{80}{-32} to lowest terms by extracting and canceling out 16.

$$t=-\frac{5}{2}$$

Now solve the equation t=\frac{0±80}{-32} when ± is minus. Reduce the fraction \frac{-80}{-32} to lowest terms by extracting and canceling out 16.

$$t=\frac{5}{2}$$

The equation is now solved.

$$t=-\frac{5}{2} t=\frac{5}{2}$$