Solve 3.68*10^-19=1/29.11*10^-31*v^2

$$3.68 \times 10 ^ { - 19 } = \frac { 1 } { 2 } 9.11 \times 10 ^ { - 31 } \times v ^ { 2 }$$

Solve for v

$$v = \frac{4000000 \sqrt{41906}}{911} \approx 898834.469106524$$

$$v = -\frac{4000000 \sqrt{41906}}{911} \approx -898834.469106524$$

Steps by Finding Square Root

Calculate 10 to the power of -19 and get \frac{1}{10000000000000000000}.

$$3.68\times \frac{1}{10000000000000000000}=\frac{1}{2}\times 9.11\times 10^{-31}v^{2}$$

Multiply 3.68 and \frac{1}{10000000000000000000} to get \frac{23}{62500000000000000000}.

$$\frac{23}{62500000000000000000}=\frac{1}{2}\times 9.11\times 10^{-31}v^{2}$$

Multiply \frac{1}{2} and 9.11 to get \frac{911}{200}.

$$\frac{23}{62500000000000000000}=\frac{911}{200}\times 10^{-31}v^{2}$$

Calculate 10 to the power of -31 and get \frac{1}{10000000000000000000000000000000}.

$$\frac{23}{62500000000000000000}=\frac{911}{200}\times \frac{1}{10000000000000000000000000000000}v^{2}$$

Multiply \frac{911}{200} and \frac{1}{10000000000000000000000000000000} to get \frac{911}{2000000000000000000000000000000000}.

$$\frac{23}{62500000000000000000}=\frac{911}{2000000000000000000000000000000000}v^{2}$$

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

$$\frac{911}{2000000000000000000000000000000000}v^{2}=\frac{23}{62500000000000000000}$$

Multiply both sides by \frac{2000000000000000000000000000000000}{911}, the reciprocal of \frac{911}{2000000000000000000000000000000000}.

$$v^{2}=\frac{23}{62500000000000000000}\times \frac{2000000000000000000000000000000000}{911}$$

Multiply \frac{23}{62500000000000000000} and \frac{2000000000000000000000000000000000}{911} to get \frac{736000000000000}{911}.

$$v^{2}=\frac{736000000000000}{911}$$

Take the square root of both sides of the equation.

$$v=\frac{4000000\sqrt{41906}}{911} v=-\frac{4000000\sqrt{41906}}{911}$$

Steps Using the Quadratic Formula

Calculate 10 to the power of -19 and get \frac{1}{10000000000000000000}.

$$3.68\times \frac{1}{10000000000000000000}=\frac{1}{2}\times 9.11\times 10^{-31}v^{2}$$

Multiply 3.68 and \frac{1}{10000000000000000000} to get \frac{23}{62500000000000000000}.

$$\frac{23}{62500000000000000000}=\frac{1}{2}\times 9.11\times 10^{-31}v^{2}$$

Multiply \frac{1}{2} and 9.11 to get \frac{911}{200}.

$$\frac{23}{62500000000000000000}=\frac{911}{200}\times 10^{-31}v^{2}$$

Calculate 10 to the power of -31 and get \frac{1}{10000000000000000000000000000000}.

$$\frac{23}{62500000000000000000}=\frac{911}{200}\times \frac{1}{10000000000000000000000000000000}v^{2}$$

Multiply \frac{911}{200} and \frac{1}{10000000000000000000000000000000} to get \frac{911}{2000000000000000000000000000000000}.

$$\frac{23}{62500000000000000000}=\frac{911}{2000000000000000000000000000000000}v^{2}$$

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

$$\frac{911}{2000000000000000000000000000000000}v^{2}=\frac{23}{62500000000000000000}$$

Subtract \frac{23}{62500000000000000000} from both sides.

$$\frac{911}{2000000000000000000000000000000000}v^{2}-\frac{23}{62500000000000000000}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{911}{2000000000000000000000000000000000} for a, 0 for b, and -\frac{23}{62500000000000000000} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{0±\sqrt{0^{2}-4\times \frac{911}{2000000000000000000000000000000000}\left(-\frac{23}{62500000000000000000}\right)}}{2\times \frac{911}{2000000000000000000000000000000000}}$$

Square 0.

$$v=\frac{0±\sqrt{-4\times \frac{911}{2000000000000000000000000000000000}\left(-\frac{23}{62500000000000000000}\right)}}{2\times \frac{911}{2000000000000000000000000000000000}}$$

Multiply -4 times \frac{911}{2000000000000000000000000000000000}.

$$v=\frac{0±\sqrt{-\frac{911}{500000000000000000000000000000000}\left(-\frac{23}{62500000000000000000}\right)}}{2\times \frac{911}{2000000000000000000000000000000000}}$$

Multiply -\frac{911}{500000000000000000000000000000000} times -\frac{23}{62500000000000000000} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$v=\frac{0±\sqrt{\frac{20953}{31250000000000000000000000000000000000000000000000000}}}{2\times \frac{911}{2000000000000000000000000000000000}}$$

Take the square root of \frac{20953}{31250000000000000000000000000000000000000000000000000}.

$$v=\frac{0±\frac{\sqrt{41906}}{250000000000000000000000000}}{2\times \frac{911}{2000000000000000000000000000000000}}$$

Multiply 2 times \frac{911}{2000000000000000000000000000000000}.

$$v=\frac{0±\frac{\sqrt{41906}}{250000000000000000000000000}}{\frac{911}{1000000000000000000000000000000000}}$$

Now solve the equation v=\frac{0±\frac{\sqrt{41906}}{250000000000000000000000000}}{\frac{911}{1000000000000000000000000000000000}} when ± is plus.

$$v=\frac{4000000\sqrt{41906}}{911}$$

Now solve the equation v=\frac{0±\frac{\sqrt{41906}}{250000000000000000000000000}}{\frac{911}{1000000000000000000000000000000000}} when ± is minus.

$$v=-\frac{4000000\sqrt{41906}}{911}$$

The equation is now solved.

$$v=\frac{4000000\sqrt{41906}}{911} v=-\frac{4000000\sqrt{41906}}{911}$$