Solve e^3-1230 v^2

Question

Find the roots

v_{1} = - \frac{e 1230 e}{1230}, v_{2} = \frac{e 1230 e}{1230}

Alternative Form

v_{1} \approx - 0.127788, v_{2} \approx 0.127788

Evaluate

e^{3} - 1230 v^{2}

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

e^{3} - 1230 v^{2} = 0

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

- 1230 v^{2} = 0 - e^{3}

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

- 1230 v^{2} = - e^{3}

Change the signs on both sides of the equation

1230 v^{2} = e^{3}

Divide both sides

\frac{1230 v ^{2}}{1230} = \frac{e ^{3}}{1230}

Divide the numbers

v^{2} = \frac{e ^{3}}{1230}

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

v = \pm \frac{e ^{3}}{1230}

Simplify the expression

More Steps

Evaluate

\frac{e ^{3}}{1230}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{e ^{3}}{1230}

Simplify the radical expression

More Steps

Evaluate

e^{3}

Rewrite the exponent as a sum where one of the addends is a multiple of the index

e^{2 + 1}

Use a^{m + n} = a^{m} \times a^{n} to expand the expression

e^{2} \times e

The root of a product is equal to the product of the roots of each factor

e^{2} \times e

Reduce the index of the radical and exponent with 2

e e

\frac{e e}{1230}

Multiply by the Conjugate

\frac{e e \times 1230}{1230 \times 1230}

Multiply the numbers

More Steps

Evaluate

e \times 1230

The product of roots with the same index is equal to the root of the product

e \times 1230

Calculate the product

1230 e

\frac{e 1230 e}{1230 \times 1230}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{e 1230 e}{1230}

v = \pm \frac{e 1230 e}{1230}

Separate the equation into 2 possible cases

v = \frac{e 1230 e}{1230} v = - \frac{e 1230 e}{1230}

Solution

v_{1} = - \frac{e 1230 e}{1230}, v_{2} = \frac{e 1230 e}{1230}

Alternative Form

v_{1} \approx - 0.127788, v_{2} \approx 0.127788

Show Solution