Solve 1/2(6x-108x)-4x^3

Question

Simplify the expression

- 51 x - 4 x^{3}

Evaluate

\frac{1}{2} (6 x - 108 x) - 4 x^{3}

Subtract the terms

More Steps

Simplify

6 x - 108 x

Collect like terms by calculating the sum or difference of their coefficients

(6 - 108) x

Subtract the numbers

- 102 x

\frac{1}{2} (- 102 x) - 4 x^{3}

Solution

More Steps

Evaluate

\frac{1}{2} (- 102)

Multiplying or dividing an odd number of negative terms equals a negative

- \frac{1}{2} \times 102

Reduce the numbers

- 1 \times 51

Simplify

- 51

- 51 x - 4 x^{3}

Show Solution

Factor the expression

- x (51 + 4 x^{2})

Evaluate

\frac{1}{2} (6 x - 108 x) - 4 x^{3}

Subtract the terms

More Steps

Simplify

6 x - 108 x

Collect like terms by calculating the sum or difference of their coefficients

(6 - 108) x

Subtract the numbers

- 102 x

\frac{1}{2} (- 102 x) - 4 x^{3}

Multiply the numbers

More Steps

Evaluate

\frac{1}{2} (- 102)

Multiplying or dividing an odd number of negative terms equals a negative

- \frac{1}{2} \times 102

Reduce the numbers

- 1 \times 51

Simplify

- 51

Evaluate

- 51 x

- 51 x - 4 x^{3}

Rewrite the expression

- x \times 51 - x \times 4 x^{2}

Solution

- x (51 + 4 x^{2})

Show Solution

Find the roots

x_{1} = - \frac{51}{2} i, x_{2} = \frac{51}{2} i, x_{3} = 0

Alternative Form

x_{1} \approx - 3.570714 i, x_{2} \approx 3.570714 i, x_{3} = 0

Evaluate

\frac{1}{2} (6 x - 108 x) - 4 x^{3}

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

\frac{1}{2} (6 x - 108 x) - 4 x^{3} = 0

Subtract the terms

More Steps

Simplify

6 x - 108 x

Collect like terms by calculating the sum or difference of their coefficients

(6 - 108) x

Subtract the numbers

- 102 x

\frac{1}{2} (- 102 x) - 4 x^{3} = 0

Multiply the numbers

More Steps

Evaluate

\frac{1}{2} (- 102)

Multiplying or dividing an odd number of negative terms equals a negative

- \frac{1}{2} \times 102

Reduce the numbers

- 1 \times 51

Simplify

- 51

- 51 x - 4 x^{3} = 0

Factor the expression

- x (51 + 4 x^{2}) = 0

Divide both sides

x (51 + 4 x^{2}) = 0

Separate the equation into 2 possible cases

x = 0 51 + 4 x^{2} = 0

Solve the equation

More Steps

Evaluate

51 + 4 x^{2} = 0

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

4 x^{2} = 0 - 51

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

4 x^{2} = - 51

Divide both sides

\frac{4 x ^{2}}{4} = \frac{- 51}{4}

Divide the numbers

x^{2} = \frac{- 51}{4}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x^{2} = - \frac{51}{4}

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

x = \pm - \frac{51}{4}

Simplify the expression

More Steps

Evaluate

- \frac{51}{4}

Evaluate the power

\frac{51}{4} \times - 1

Evaluate the power

\frac{51}{4} \times i

Evaluate the power

\frac{51}{2} i

x = \pm \frac{51}{2} i

Separate the equation into 2 possible cases

x = \frac{51}{2} i x = - \frac{51}{2} i

x = 0 x = \frac{51}{2} i x = - \frac{51}{2} i

Solution

x_{1} = - \frac{51}{2} i, x_{2} = \frac{51}{2} i, x_{3} = 0

Alternative Form

x_{1} \approx - 3.570714 i, x_{2} \approx 3.570714 i, x_{3} = 0

Show Solution