Solve 4.9t^2=0.196

$$4.9 t ^ { 2 } = 0.196$$

Solve for t

$$t=0.2$$

$$t=-0.2$$

Steps Using Difference of Squares

Divide both sides by 4.9.

$$t^{2}=\frac{0.196}{4.9}$$

Expand \frac{0.196}{4.9} by multiplying both numerator and the denominator by 1000.

$$t^{2}=\frac{196}{4900}$$

Reduce the fraction \frac{196}{4900} to lowest terms by extracting and canceling out 196.

$$t^{2}=\frac{1}{25}$$

Subtract \frac{1}{25} from both sides.

$$t^{2}-\frac{1}{25}=0$$

Multiply both sides by 25.

$$25t^{2}-1=0$$

Consider 25t^{2}-1. Rewrite 25t^{2}-1 as \left(5t\right)^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(5t-1\right)\left(5t+1\right)=0$$

To find equation solutions, solve 5t-1=0 and 5t+1=0.

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

Steps by Finding Square Root

Divide both sides by 4.9.

$$t^{2}=\frac{0.196}{4.9}$$

Expand \frac{0.196}{4.9} by multiplying both numerator and the denominator by 1000.

$$t^{2}=\frac{196}{4900}$$

Reduce the fraction \frac{196}{4900} to lowest terms by extracting and canceling out 196.

$$t^{2}=\frac{1}{25}$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Divide both sides by 4.9.

$$t^{2}=\frac{0.196}{4.9}$$

Expand \frac{0.196}{4.9} by multiplying both numerator and the denominator by 1000.

$$t^{2}=\frac{196}{4900}$$

Reduce the fraction \frac{196}{4900} to lowest terms by extracting and canceling out 196.

$$t^{2}=\frac{1}{25}$$

Subtract \frac{1}{25} from both sides.

$$t^{2}-\frac{1}{25}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{1}{25} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{25}\right)}}{2}$$

Square 0.

$$t=\frac{0±\sqrt{-4\left(-\frac{1}{25}\right)}}{2}$$

Multiply -4 times -\frac{1}{25}.

$$t=\frac{0±\sqrt{\frac{4}{25}}}{2}$$

Take the square root of \frac{4}{25}.

$$t=\frac{0±\frac{2}{5}}{2}$$

Now solve the equation t=\frac{0±\frac{2}{5}}{2} when ± is plus.

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

Now solve the equation t=\frac{0±\frac{2}{5}}{2} when ± is minus.

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

The equation is now solved.

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