Solve 250v^2=241960

$$250 v ^ { 2 } = 241960$$

Solve for v

$$v = \frac{2 \sqrt{6049}}{5} \approx 31.110126969$$

$$v = -\frac{2 \sqrt{6049}}{5} \approx -31.110126969$$

Steps by Finding Square Root

Divide both sides by 250.

$$v^{2}=\frac{241960}{250}$$

Reduce the fraction \frac{241960}{250} to lowest terms by extracting and canceling out 10.

$$v^{2}=\frac{24196}{25}$$

Take the square root of both sides of the equation.

$$v=\frac{2\sqrt{6049}}{5} v=-\frac{2\sqrt{6049}}{5}$$

Steps Using the Quadratic Formula

Divide both sides by 250.

$$v^{2}=\frac{241960}{250}$$

Reduce the fraction \frac{241960}{250} to lowest terms by extracting and canceling out 10.

$$v^{2}=\frac{24196}{25}$$

Subtract \frac{24196}{25} from both sides.

$$v^{2}-\frac{24196}{25}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{24196}{25} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{0±\sqrt{0^{2}-4\left(-\frac{24196}{25}\right)}}{2}$$

Square 0.

$$v=\frac{0±\sqrt{-4\left(-\frac{24196}{25}\right)}}{2}$$

Multiply -4 times -\frac{24196}{25}.

$$v=\frac{0±\sqrt{\frac{96784}{25}}}{2}$$

Take the square root of \frac{96784}{25}.

$$v=\frac{0±\frac{4\sqrt{6049}}{5}}{2}$$

Now solve the equation v=\frac{0±\frac{4\sqrt{6049}}{5}}{2} when ± is plus.

$$v=\frac{2\sqrt{6049}}{5}$$

Now solve the equation v=\frac{0±\frac{4\sqrt{6049}}{5}}{2} when ± is minus.

$$v=-\frac{2\sqrt{6049}}{5}$$

The equation is now solved.

$$v=\frac{2\sqrt{6049}}{5} v=-\frac{2\sqrt{6049}}{5}$$