Solve x^3-6x^211x-6

Question

Simplify the expression

- 65 x^{3} - 6

Evaluate

x^{3} - 6 x^{2} \times 11 x - 6

Multiply

More Steps

Multiply the terms

- 6 x^{2} \times 11 x

Multiply the terms

- 66 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 66 x^{2 + 1}

Add the numbers

- 66 x^{3}

x^{3} - 66 x^{3} - 6

Solution

More Steps

Evaluate

x^{3} - 66 x^{3}

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

(1 - 66) x^{3}

Subtract the numbers

- 65 x^{3}

- 65 x^{3} - 6

Show Solution

Find the roots

x = - \frac{3 25350}{65}

Alternative Form

x \approx - 0.451938

Evaluate

x^{3} - 6 x^{2} \times 11 x - 6

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

x^{3} - 6 x^{2} \times 11 x - 6 = 0

Multiply

More Steps

Multiply the terms

6 x^{2} \times 11 x

Multiply the terms

66 x^{2} \times x

Multiply the terms with the same base by adding their exponents

66 x^{2 + 1}

Add the numbers

66 x^{3}

x^{3} - 66 x^{3} - 6 = 0

Subtract the terms

More Steps

Simplify

x^{3} - 66 x^{3}

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

(1 - 66) x^{3}

Subtract the numbers

- 65 x^{3}

- 65 x^{3} - 6 = 0

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

- 65 x^{3} = 0 + 6

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

- 65 x^{3} = 6

Change the signs on both sides of the equation

65 x^{3} = - 6

Divide both sides

\frac{65 x ^{3}}{65} = \frac{- 6}{65}

Divide the numbers

x^{3} = \frac{- 6}{65}

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

x^{3} = - \frac{6}{65}

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

3 x^{3} = 3 - \frac{6}{65}

Calculate

x = 3 - \frac{6}{65}

Solution

More Steps

Evaluate

3 - \frac{6}{65}

An odd root of a negative radicand is always a negative

- 3 \frac{6}{65}

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

- \frac{3 6}{3 65}

Multiply by the Conjugate

\frac{- 3 6 \times 3 6 5 ^{2}}{3 65 \times 3 6 5 ^{2}}

Simplify

\frac{- 3 6 \times 3 4225}{3 65 \times 3 6 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 36 \times 34225

The product of roots with the same index is equal to the root of the product

- 3 6 \times 4225

Calculate the product

- 325350

\frac{- 3 25350}{3 65 \times 3 6 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

365 \times 3 6 5^{2}

The product of roots with the same index is equal to the root of the product

3 65 \times 6 5^{2}

Calculate the product

3 6 5^{3}

Reduce the index of the radical and exponent with 3

65

\frac{- 3 25350}{65}

Calculate

- \frac{3 25350}{65}

x = - \frac{3 25350}{65}

Alternative Form

x \approx - 0.451938

Show Solution