Solve (3v 9)-(2v^5)

Question

Simplify the expression

27 v - 2 v^{5}

Evaluate

(3 v \times 9) - 2 v^{5}

Solution

27 v - 2 v^{5}

Show Solution

v (27 - 2 v^{4})

Evaluate

(3 v \times 9) - 2 v^{5}

Multiply the terms

27 v - 2 v^{5}

Rewrite the expression

v \times 27 - v \times 2 v^{4}

Solution

v (27 - 2 v^{4})

Show Solution

v_{1} = - \frac{4 216}{2}, v_{2} = 0, v_{3} = \frac{4 216}{2}

Alternative Form

v_{1} \approx - 1.916829, v_{2} = 0, v_{3} \approx 1.916829

Evaluate

(3 v \times 9) - (2 v^{5})

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

(3 v \times 9) - (2 v^{5}) = 0

Multiply the terms

27 v - (2 v^{5}) = 0

Multiply the terms

27 v - 2 v^{5} = 0

Factor the expression

v (27 - 2 v^{4}) = 0

Separate the equation into 2 possible cases

v = 0 27 - 2 v^{4} = 0

Solve the equation

More Steps

Evaluate

27 - 2 v^{4} = 0

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

- 2 v^{4} = 0 - 27

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

- 2 v^{4} = - 27

Change the signs on both sides of the equation

2 v^{4} = 27

Divide both sides

\frac{2 v ^{4}}{2} = \frac{27}{2}

Divide the numbers

v^{4} = \frac{27}{2}

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

v = \pm 4 \frac{27}{2}

Simplify the expression

More Steps

Evaluate

4 \frac{27}{2}

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

\frac{4 27}{4 2}

Multiply by the Conjugate

\frac{4 27 \times 4 2 ^{3}}{4 2 \times 4 2 ^{3}}

Simplify

\frac{4 27 \times 4 8}{4 2 \times 4 2 ^{3}}

Multiply the numbers

\frac{4 216}{4 2 \times 4 2 ^{3}}

Multiply the numbers

\frac{4 216}{2}

v = \pm \frac{4 216}{2}

Separate the equation into 2 possible cases

v = \frac{4 216}{2} v = - \frac{4 216}{2}

v = 0 v = \frac{4 216}{2} v = - \frac{4 216}{2}

Solution

v_{1} = - \frac{4 216}{2}, v_{2} = 0, v_{3} = \frac{4 216}{2}

Alternative Form

v_{1} \approx - 1.916829, v_{2} = 0, v_{3} \approx 1.916829

Show Solution