Solve e^5-1660 v^2

Question

Find the roots

v_{1} = - \frac{e ^{2} 415 e}{830}, v_{2} = \frac{e ^{2} 415 e}{830}

Alternative Form

v_{1} \approx - 0.299008, v_{2} \approx 0.299008

Evaluate

e^{5} - 1660 v^{2}

To find the roots of the expression,set the expression equal to 0

e^{5} - 1660 v^{2} = 0

Move the constant to the right-hand side and change its sign

- 1660 v^{2} = 0 - e^{5}

Removing 0 doesn't change the value,so remove it from the expression

- 1660 v^{2} = - e^{5}

Change the signs on both sides of the equation

1660 v^{2} = e^{5}

Divide both sides

\frac{1660 v ^{2}}{1660} = \frac{e ^{5}}{1660}

Divide the numbers

v^{2} = \frac{e ^{5}}{1660}

Take the root of both sides of the equation and remember to use both positive and negative roots

v = \pm \frac{e ^{5}}{1660}

Simplify the expression

More Steps

v = \pm \frac{e ^{2} 415 e}{830}

Separate the equation into 2 possible cases

v = \frac{e ^{2} 415 e}{830} v = - \frac{e ^{2} 415 e}{830}

Solution

v_{1} = - \frac{e ^{2} 415 e}{830}, v_{2} = \frac{e ^{2} 415 e}{830}

Alternative Form

v_{1} \approx - 0.299008, v_{2} \approx 0.299008

Show Solution