Solve 120=-16t^2+95

$$120 = - 16 t ^ { 2 } + 95$$

Solve for t

$$t=-\frac{5}{4}i=-1.25i$$

$$t=\frac{5}{4}i=1.25i$$

Steps by Finding Square Root

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

$$-16t^{2}+95=120$$

Subtract 95 from both sides.

$$-16t^{2}=120-95$$

Subtract 95 from 120 to get 25.

$$-16t^{2}=25$$

Divide both sides by -16.

$$t^{2}=-\frac{25}{16}$$

The equation is now solved.

$$t=\frac{5}{4}i t=-\frac{5}{4}i$$

Steps Using the Quadratic Formula

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

$$-16t^{2}+95=120$$

Subtract 120 from both sides.

$$-16t^{2}+95-120=0$$

Subtract 120 from 95 to get -25.

$$-16t^{2}-25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -16 for a, 0 for b, and -25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\left(-16\right)\left(-25\right)}}{2\left(-16\right)}$$

Square 0.

$$t=\frac{0±\sqrt{-4\left(-16\right)\left(-25\right)}}{2\left(-16\right)}$$

Multiply -4 times -16.

$$t=\frac{0±\sqrt{64\left(-25\right)}}{2\left(-16\right)}$$

Multiply 64 times -25.

$$t=\frac{0±\sqrt{-1600}}{2\left(-16\right)}$$

Take the square root of -1600.

$$t=\frac{0±40i}{2\left(-16\right)}$$

Multiply 2 times -16.

$$t=\frac{0±40i}{-32}$$

Now solve the equation t=\frac{0±40i}{-32} when ± is plus.

$$t=-\frac{5}{4}i$$

Now solve the equation t=\frac{0±40i}{-32} when ± is minus.

$$t=\frac{5}{4}i$$

The equation is now solved.

$$t=-\frac{5}{4}i t=\frac{5}{4}i$$