Solve 19.6=9.8/2t^2

$$19.6 = \frac { 9.8 } { 2 } t ^ { 2 }$$

Solve for t

$$t=2$$

$$t=-2$$

Steps Using Difference of Squares

Expand \frac{9.8}{2} by multiplying both numerator and the denominator by 10.

$$19.6=\frac{98}{20}t^{2}$$

Reduce the fraction \frac{98}{20} to lowest terms by extracting and canceling out 2.

$$19.6=\frac{49}{10}t^{2}$$

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

$$\frac{49}{10}t^{2}=19.6$$

Subtract 19.6 from both sides.

$$\frac{49}{10}t^{2}-19.6=0$$

Multiply both sides by 10.

$$49t^{2}-196=0$$

Consider 49t^{2}-196. Rewrite 49t^{2}-196 as \left(7t\right)^{2}-14^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(7t-14\right)\left(7t+14\right)=0$$

To find equation solutions, solve 7t-14=0 and 7t+14=0.

$$t=2 t=-2$$

Steps by Finding Square Root

Expand \frac{9.8}{2} by multiplying both numerator and the denominator by 10.

$$19.6=\frac{98}{20}t^{2}$$

Reduce the fraction \frac{98}{20} to lowest terms by extracting and canceling out 2.

$$19.6=\frac{49}{10}t^{2}$$

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

$$\frac{49}{10}t^{2}=19.6$$

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

$$t^{2}=19.6\times \frac{10}{49}$$

Multiply 19.6 and \frac{10}{49} to get 4.

$$t^{2}=4$$

Take the square root of both sides of the equation.

$$t=2 t=-2$$

Steps Using the Quadratic Formula

Expand \frac{9.8}{2} by multiplying both numerator and the denominator by 10.

$$19.6=\frac{98}{20}t^{2}$$

Reduce the fraction \frac{98}{20} to lowest terms by extracting and canceling out 2.

$$19.6=\frac{49}{10}t^{2}$$

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

$$\frac{49}{10}t^{2}=19.6$$

Subtract 19.6 from both sides.

$$\frac{49}{10}t^{2}-19.6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{49}{10} for a, 0 for b, and -19.6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\times \frac{49}{10}\left(-19.6\right)}}{2\times \frac{49}{10}}$$

Square 0.

$$t=\frac{0±\sqrt{-4\times \frac{49}{10}\left(-19.6\right)}}{2\times \frac{49}{10}}$$

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

$$t=\frac{0±\sqrt{-\frac{98}{5}\left(-19.6\right)}}{2\times \frac{49}{10}}$$

Multiply -\frac{98}{5} times -19.6 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$t=\frac{0±\sqrt{\frac{9604}{25}}}{2\times \frac{49}{10}}$$

Take the square root of \frac{9604}{25}.

$$t=\frac{0±\frac{98}{5}}{2\times \frac{49}{10}}$$

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

$$t=\frac{0±\frac{98}{5}}{\frac{49}{5}}$$

Now solve the equation t=\frac{0±\frac{98}{5}}{\frac{49}{5}} when ± is plus.

$$t=2$$

Now solve the equation t=\frac{0±\frac{98}{5}}{\frac{49}{5}} when ± is minus.

$$t=-2$$

The equation is now solved.

$$t=2 t=-2$$