Solve v^2=5000/37

$$v ^ { 2 } = \frac { 5000 } { 37 }$$

Solve for v

$$v = \frac{50 \sqrt{74}}{37} \approx 11.624763874$$

$$v = -\frac{50 \sqrt{74}}{37} \approx -11.624763874$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$v=\frac{50\sqrt{74}}{37} v=-\frac{50\sqrt{74}}{37}$$

Steps Using the Quadratic Formula

Subtract \frac{5000}{37} from both sides.

$$v^{2}-\frac{5000}{37}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{5000}{37} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{0±\sqrt{0^{2}-4\left(-\frac{5000}{37}\right)}}{2}$$

Square 0.

$$v=\frac{0±\sqrt{-4\left(-\frac{5000}{37}\right)}}{2}$$

Multiply -4 times -\frac{5000}{37}.

$$v=\frac{0±\sqrt{\frac{20000}{37}}}{2}$$

Take the square root of \frac{20000}{37}.

$$v=\frac{0±\frac{100\sqrt{74}}{37}}{2}$$

Now solve the equation v=\frac{0±\frac{100\sqrt{74}}{37}}{2} when ± is plus.

$$v=\frac{50\sqrt{74}}{37}$$

Now solve the equation v=\frac{0±\frac{100\sqrt{74}}{37}}{2} when ± is minus.

$$v=-\frac{50\sqrt{74}}{37}$$

The equation is now solved.

$$v=\frac{50\sqrt{74}}{37} v=-\frac{50\sqrt{74}}{37}$$