Solve -x^4 6x^2-3x

Question

Simplify the expression

- 6 x^{6} - 3 x

Evaluate

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

Solution

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

- x^{4 + 2} \times 6

Add the numbers

- x^{6} \times 6

Use the commutative property to reorder the terms

- 6 x^{6}

- 6 x^{6} - 3 x

Show Solution

Factor the expression

- 3 x (2 x^{5} + 1)

Evaluate

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

Multiply

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

x^{4 + 2} \times 6

Add the numbers

x^{6} \times 6

Use the commutative property to reorder the terms

6 x^{6}

- 6 x^{6} - 3 x

Rewrite the expression

- 3 x \times 2 x^{5} - 3 x

Solution

- 3 x (2 x^{5} + 1)

Show Solution

Find the roots

x_{1} = - \frac{5 16}{2}, x_{2} = 0

Alternative Form

x_{1} \approx - 0.870551, x_{2} = 0

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

x^{4 + 2} \times 6

Add the numbers

x^{6} \times 6

Use the commutative property to reorder the terms

6 x^{6}

- 6 x^{6} - 3 x = 0

Factor the expression

- 3 x (2 x^{5} + 1) = 0

Divide both sides

x (2 x^{5} + 1) = 0

Separate the equation into 2 possible cases

x = 0 2 x^{5} + 1 = 0

Solve the equation

More Steps

Evaluate

2 x^{5} + 1 = 0

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

2 x^{5} = 0 - 1

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

2 x^{5} = - 1

Divide both sides

\frac{2 x ^{5}}{2} = \frac{- 1}{2}

Divide the numbers

x^{5} = \frac{- 1}{2}

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

x^{5} = - \frac{1}{2}

Take the 5 -th root on both sides of the equation

5 x^{5} = 5 - \frac{1}{2}

Calculate

x = 5 - \frac{1}{2}

Simplify the root

More Steps

Evaluate

5 - \frac{1}{2}

An odd root of a negative radicand is always a negative

- 5 \frac{1}{2}

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

- \frac{5 1}{5 2}

Simplify the radical expression

- \frac{1}{5 2}

Multiply by the Conjugate

\frac{- 5 2 ^{4}}{5 2 \times 5 2 ^{4}}

Simplify

\frac{- 5 16}{5 2 \times 5 2 ^{4}}

Multiply the numbers

\frac{- 5 16}{2}

Calculate

- \frac{5 16}{2}

x = - \frac{5 16}{2}

x = 0 x = - \frac{5 16}{2}

Solution

x_{1} = - \frac{5 16}{2}, x_{2} = 0

Alternative Form

x_{1} \approx - 0.870551, x_{2} = 0

Show Solution