Solve (-6x^3 4x^2 -7x)

Question

Simplify the expression

- 24 x^{5} - 7 x

Evaluate

- 6 x^{3} \times 4 x^{2} - 7 x

Solution

More Steps

Evaluate

- 6 x^{3} \times 4 x^{2}

Multiply the terms

- 24 x^{3} \times x^{2}

Multiply the terms with the same base by adding their exponents

- 24 x^{3 + 2}

Add the numbers

- 24 x^{5}

- 24 x^{5} - 7 x

Show Solution

Factor the expression

- x (24 x^{4} + 7)

Evaluate

- 6 x^{3} \times 4 x^{2} - 7 x

Multiply

More Steps

Evaluate

- 6 x^{3} \times 4 x^{2}

Multiply the terms

- 24 x^{3} \times x^{2}

Multiply the terms with the same base by adding their exponents

- 24 x^{3 + 2}

Add the numbers

- 24 x^{5}

- 24 x^{5} - 7 x

Rewrite the expression

- x \times 24 x^{4} - x \times 7

Solution

- x (24 x^{4} + 7)

Show Solution

Find the roots

x_{1} = - \frac{4 1512}{12} - \frac{4 1512}{12} i, x_{2} = \frac{4 1512}{12} + \frac{4 1512}{12} i, x_{3} = 0

Alternative Form

x_{1} \approx - 0.519645 - 0.519645 i, x_{2} \approx 0.519645 + 0.519645 i, x_{3} = 0

Evaluate

(- 6 x^{3} \times 4 x^{2} - 7 x)

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

- 6 x^{3} \times 4 x^{2} - 7 x = 0

Multiply

More Steps

Multiply the terms

- 6 x^{3} \times 4 x^{2}

Multiply the terms

- 24 x^{3} \times x^{2}

Multiply the terms with the same base by adding their exponents

- 24 x^{3 + 2}

Add the numbers

- 24 x^{5}

- 24 x^{5} - 7 x = 0

Factor the expression

- x (24 x^{4} + 7) = 0

Divide both sides

x (24 x^{4} + 7) = 0

Separate the equation into 2 possible cases

x = 0 24 x^{4} + 7 = 0

Solve the equation

More Steps

Evaluate

24 x^{4} + 7 = 0

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

24 x^{4} = 0 - 7

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

24 x^{4} = - 7

Divide both sides

\frac{24 x ^{4}}{24} = \frac{- 7}{24}

Divide the numbers

x^{4} = \frac{- 7}{24}

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

x^{4} = - \frac{7}{24}

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

x = \pm 4 - \frac{7}{24}

Simplify the expression

More Steps

Evaluate

4 - \frac{7}{24}

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

\frac{4 - 7}{4 24}

Simplify the radical expression

\frac{\frac{4 28}{2} + \frac{4 28}{2} i}{4 24}

Simplify

\frac{4 7}{2 4 6} + \frac{4 7}{2 4 6} i

Rearrange the numbers

\frac{4 1512}{12} + \frac{4 7}{2 4 6} i

Rearrange the numbers

\frac{4 1512}{12} + \frac{4 1512}{12} i

x = \pm (\frac{4 1512}{12} + \frac{4 1512}{12} i)

Separate the equation into 2 possible cases

x = \frac{4 1512}{12} + \frac{4 1512}{12} i x = - \frac{4 1512}{12} - \frac{4 1512}{12} i

x = 0 x = \frac{4 1512}{12} + \frac{4 1512}{12} i x = - \frac{4 1512}{12} - \frac{4 1512}{12} i

Solution

x_{1} = - \frac{4 1512}{12} - \frac{4 1512}{12} i, x_{2} = \frac{4 1512}{12} + \frac{4 1512}{12} i, x_{3} = 0

Alternative Form

x_{1} \approx - 0.519645 - 0.519645 i, x_{2} \approx 0.519645 + 0.519645 i, x_{3} = 0

Show Solution