Solve x^3-3x^2 6x-8

Question

Simplify the expression

- 17 x^{3} - 8

Evaluate

x^{3} - 3 x^{2} \times 6 x - 8

Multiply

More Steps

Multiply the terms

- 3 x^{2} \times 6 x

Multiply the terms

- 18 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 18 x^{2 + 1}

Add the numbers

- 18 x^{3}

x^{3} - 18 x^{3} - 8

Solution

More Steps

Evaluate

x^{3} - 18 x^{3}

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

(1 - 18) x^{3}

Subtract the numbers

- 17 x^{3}

- 17 x^{3} - 8

Show Solution

Find the roots

x = - \frac{2 3 289}{17}

Alternative Form

x \approx - 0.777822

Evaluate

x^{3} - 3 x^{2} \times 6 x - 8

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

x^{3} - 3 x^{2} \times 6 x - 8 = 0

Multiply

More Steps

Multiply the terms

3 x^{2} \times 6 x

Multiply the terms

18 x^{2} \times x

Multiply the terms with the same base by adding their exponents

18 x^{2 + 1}

Add the numbers

18 x^{3}

x^{3} - 18 x^{3} - 8 = 0

Subtract the terms

More Steps

Simplify

x^{3} - 18 x^{3}

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

(1 - 18) x^{3}

Subtract the numbers

- 17 x^{3}

- 17 x^{3} - 8 = 0

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

- 17 x^{3} = 0 + 8

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

- 17 x^{3} = 8

Change the signs on both sides of the equation

17 x^{3} = - 8

Divide both sides

\frac{17 x ^{3}}{17} = \frac{- 8}{17}

Divide the numbers

x^{3} = \frac{- 8}{17}

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

x^{3} = - \frac{8}{17}

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

3 x^{3} = 3 - \frac{8}{17}

Calculate

x = 3 - \frac{8}{17}

Solution

More Steps

Evaluate

3 - \frac{8}{17}

An odd root of a negative radicand is always a negative

- 3 \frac{8}{17}

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

- \frac{3 8}{3 17}

Simplify the radical expression

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Evaluate

38

Write the number in exponential form with the base of 2

3 2^{3}

Reduce the index of the radical and exponent with 3

2

- \frac{2}{3 17}

Multiply by the Conjugate

\frac{- 2 3 1 7 ^{2}}{3 17 \times 3 1 7 ^{2}}

Simplify

\frac{- 2 3 289}{3 17 \times 3 1 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

317 \times 3 1 7^{2}

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

3 17 \times 1 7^{2}

Calculate the product

3 1 7^{3}

Reduce the index of the radical and exponent with 3

17

\frac{- 2 3 289}{17}

Calculate

- \frac{2 3 289}{17}

x = - \frac{2 3 289}{17}

Alternative Form

x \approx - 0.777822

Show Solution