Solve 9.8=0.25*v^2/1

$$9.8 = 0.25 \times \frac { v ^ { 2 } } { 1 }$$

Solve for v

$$v = \frac{14 \sqrt{5}}{5} \approx 6.260990337$$

$$v = -\frac{14 \sqrt{5}}{5} \approx -6.260990337$$

Steps by Finding Square Root

Divide both sides by 0.25.

$$\frac{9.8}{0.25}=\frac{v^{2}}{1}$$

Expand \frac{9.8}{0.25} by multiplying both numerator and the denominator by 100.

$$\frac{980}{25}=\frac{v^{2}}{1}$$

Reduce the fraction \frac{980}{25} to lowest terms by extracting and canceling out 5.

$$\frac{196}{5}=\frac{v^{2}}{1}$$

Multiply both sides by 1.

$$\frac{196}{5}\times 1=v^{2}$$

Multiply \frac{196}{5} and 1 to get \frac{196}{5}.

$$\frac{196}{5}=v^{2}$$

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

$$v^{2}=\frac{196}{5}$$

Take the square root of both sides of the equation.

$$v=\frac{14\sqrt{5}}{5} v=-\frac{14\sqrt{5}}{5}$$

Steps Using the Quadratic Formula

Divide both sides by 0.25.

$$\frac{9.8}{0.25}=\frac{v^{2}}{1}$$

Expand \frac{9.8}{0.25} by multiplying both numerator and the denominator by 100.

$$\frac{980}{25}=\frac{v^{2}}{1}$$

Reduce the fraction \frac{980}{25} to lowest terms by extracting and canceling out 5.

$$\frac{196}{5}=\frac{v^{2}}{1}$$

Multiply both sides by 1.

$$\frac{196}{5}\times 1=v^{2}$$

Multiply \frac{196}{5} and 1 to get \frac{196}{5}.

$$\frac{196}{5}=v^{2}$$

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

$$v^{2}=\frac{196}{5}$$

Subtract \frac{196}{5} from both sides.

$$v^{2}-\frac{196}{5}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{196}{5} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{0±\sqrt{0^{2}-4\left(-\frac{196}{5}\right)}}{2}$$

Square 0.

$$v=\frac{0±\sqrt{-4\left(-\frac{196}{5}\right)}}{2}$$

Multiply -4 times -\frac{196}{5}.

$$v=\frac{0±\sqrt{\frac{784}{5}}}{2}$$

Take the square root of \frac{784}{5}.

$$v=\frac{0±\frac{28\sqrt{5}}{5}}{2}$$

Now solve the equation v=\frac{0±\frac{28\sqrt{5}}{5}}{2} when ± is plus.

$$v=\frac{14\sqrt{5}}{5}$$

Now solve the equation v=\frac{0±\frac{28\sqrt{5}}{5}}{2} when ± is minus.

$$v=-\frac{14\sqrt{5}}{5}$$

The equation is now solved.

$$v=\frac{14\sqrt{5}}{5} v=-\frac{14\sqrt{5}}{5}$$