Solve -12.5=14.36+-1/2*9.8*t^2

$$- 12.5 = 14.36 + - \frac { 1 } { 2 } \times 9.8 \times t ^ { 2 }$$

Solve for t

$$t = \frac{\sqrt{6715}}{35} \approx 2.341288674$$

$$t = -\frac{\sqrt{6715}}{35} \approx -2.341288674$$

Steps by Finding Square Root

Multiply -\frac{1}{2} and 9.8 to get -\frac{49}{10}.

$$-12.5=14.36-\frac{49}{10}t^{2}$$

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

$$14.36-\frac{49}{10}t^{2}=-12.5$$

Subtract 14.36 from both sides.

$$-\frac{49}{10}t^{2}=-12.5-14.36$$

Subtract 14.36 from -12.5 to get -26.86.

$$-\frac{49}{10}t^{2}=-26.86$$

Multiply both sides by -\frac{10}{49}, the reciprocal of -\frac{49}{10}.

$$t^{2}=-26.86\left(-\frac{10}{49}\right)$$

Multiply -26.86 and -\frac{10}{49} to get \frac{1343}{245}.

$$t^{2}=\frac{1343}{245}$$

Take the square root of both sides of the equation.

$$t=\frac{\sqrt{6715}}{35} t=-\frac{\sqrt{6715}}{35}$$

Steps Using the Quadratic Formula

Multiply -\frac{1}{2} and 9.8 to get -\frac{49}{10}.

$$-12.5=14.36-\frac{49}{10}t^{2}$$

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

$$14.36-\frac{49}{10}t^{2}=-12.5$$

Add 12.5 to both sides.

$$14.36-\frac{49}{10}t^{2}+12.5=0$$

Add 14.36 and 12.5 to get 26.86.

$$26.86-\frac{49}{10}t^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-\frac{49}{10}t^{2}+26.86=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{49}{10} for a, 0 for b, and 26.86 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\left(-\frac{49}{10}\right)\times 26.86}}{2\left(-\frac{49}{10}\right)}$$

Square 0.

$$t=\frac{0±\sqrt{-4\left(-\frac{49}{10}\right)\times 26.86}}{2\left(-\frac{49}{10}\right)}$$

Multiply -4 times -\frac{49}{10}.

$$t=\frac{0±\sqrt{\frac{98}{5}\times 26.86}}{2\left(-\frac{49}{10}\right)}$$

Multiply \frac{98}{5} times 26.86 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$t=\frac{0±\sqrt{\frac{65807}{125}}}{2\left(-\frac{49}{10}\right)}$$

Take the square root of \frac{65807}{125}.

$$t=\frac{0±\frac{7\sqrt{6715}}{25}}{2\left(-\frac{49}{10}\right)}$$

Multiply 2 times -\frac{49}{10}.

$$t=\frac{0±\frac{7\sqrt{6715}}{25}}{-\frac{49}{5}}$$

Now solve the equation t=\frac{0±\frac{7\sqrt{6715}}{25}}{-\frac{49}{5}} when ± is plus.

$$t=-\frac{\sqrt{6715}}{35}$$

Now solve the equation t=\frac{0±\frac{7\sqrt{6715}}{25}}{-\frac{49}{5}} when ± is minus.

$$t=\frac{\sqrt{6715}}{35}$$

The equation is now solved.

$$t=-\frac{\sqrt{6715}}{35} t=\frac{\sqrt{6715}}{35}$$