Solve (x-1)(-x^2 5x-1)

Question

Simplify the expression

- 5 x^{4} - x + 5 x^{3} + 1

Evaluate

(x - 1) (- x^{2} \times 5 x - 1)

Multiply

More Steps

Evaluate

- x^{2} \times 5 x

Multiply the terms with the same base by adding their exponents

- x^{2 + 1} \times 5

Add the numbers

- x^{3} \times 5

Use the commutative property to reorder the terms

- 5 x^{3}

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

Apply the distributive property

x (- 5 x^{3}) - x \times 1 - (- 5 x^{3}) - (- 1)

Multiply the terms

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Evaluate

x (- 5 x^{3})

Use the commutative property to reorder the terms

- 5 x \times x^{3}

Multiply the terms

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Evaluate

x \times x^{3}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{1 + 3}

Add the numbers

x^{4}

- 5 x^{4}

- 5 x^{4} - x \times 1 - (- 5 x^{3}) - (- 1)

Any expression multiplied by 1 remains the same

- 5 x^{4} - x - (- 5 x^{3}) - (- 1)

When there is - in front of an expression in parentheses change the sign of each term of the expression and remove the parentheses

- 5 x^{4} - x + 5 x^{3} - (- 1)

Solution

- 5 x^{4} - x + 5 x^{3} + 1

Show Solution

Find the roots

x_{1} = - \frac{3 25}{5}, x_{2} = 1

Alternative Form

x_{1} \approx - 0.584804, x_{2} = 1

Evaluate

(x - 1) (- x^{2} \times 5 x - 1)

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

(x - 1) (- x^{2} \times 5 x - 1) = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 5 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 5

Add the numbers

x^{3} \times 5

Use the commutative property to reorder the terms

5 x^{3}

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

Separate the equation into 2 possible cases

x - 1 = 0 - 5 x^{3} - 1 = 0

Solve the equation

More Steps

Evaluate

x - 1 = 0

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

x = 0 + 1

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

x = 1

x = 1 - 5 x^{3} - 1 = 0

Solve the equation

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Evaluate

- 5 x^{3} - 1 = 0

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

- 5 x^{3} = 0 + 1

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

- 5 x^{3} = 1

Change the signs on both sides of the equation

5 x^{3} = - 1

Divide both sides

\frac{5 x ^{3}}{5} = \frac{- 1}{5}

Divide the numbers

x^{3} = \frac{- 1}{5}

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

x^{3} = - \frac{1}{5}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 - \frac{1}{5}

Calculate

x = 3 - \frac{1}{5}

Simplify the root

More Steps

Evaluate

3 - \frac{1}{5}

An odd root of a negative radicand is always a negative

- 3 \frac{1}{5}

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

- \frac{3 1}{3 5}

Simplify the radical expression

- \frac{1}{3 5}

Multiply by the Conjugate

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

Simplify

\frac{- 3 25}{3 5 \times 3 5 ^{2}}

Multiply the numbers

\frac{- 3 25}{5}

Calculate

- \frac{3 25}{5}

x = - \frac{3 25}{5}

x = 1 x = - \frac{3 25}{5}

Solution

x_{1} = - \frac{3 25}{5}, x_{2} = 1

Alternative Form

x_{1} \approx - 0.584804, x_{2} = 1

Show Solution