Solve x^3-6x^2 12x-8

Question

Simplify the expression

- 71 x^{3} - 8

Evaluate

x^{3} - 6 x^{2} \times 12 x - 8

Multiply

More Steps

Multiply the terms

- 6 x^{2} \times 12 x

Multiply the terms

- 72 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 72 x^{2 + 1}

Add the numbers

- 72 x^{3}

x^{3} - 72 x^{3} - 8

Solution

More Steps

Evaluate

x^{3} - 72 x^{3}

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

(1 - 72) x^{3}

Subtract the numbers

- 71 x^{3}

- 71 x^{3} - 8

Show Solution

Find the roots

x = - \frac{2 3 5041}{71}

Alternative Form

x \approx - 0.482996

Evaluate

x^{3} - 6 x^{2} \times 12 x - 8

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

x^{3} - 6 x^{2} \times 12 x - 8 = 0

Multiply

More Steps

Multiply the terms

6 x^{2} \times 12 x

Multiply the terms

72 x^{2} \times x

Multiply the terms with the same base by adding their exponents

72 x^{2 + 1}

Add the numbers

72 x^{3}

x^{3} - 72 x^{3} - 8 = 0

Subtract the terms

More Steps

Simplify

x^{3} - 72 x^{3}

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

(1 - 72) x^{3}

Subtract the numbers

- 71 x^{3}

- 71 x^{3} - 8 = 0

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

- 71 x^{3} = 0 + 8

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

- 71 x^{3} = 8

Change the signs on both sides of the equation

71 x^{3} = - 8

Divide both sides

\frac{71 x ^{3}}{71} = \frac{- 8}{71}

Divide the numbers

x^{3} = \frac{- 8}{71}

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

x^{3} = - \frac{8}{71}

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

3 x^{3} = 3 - \frac{8}{71}

Calculate

x = 3 - \frac{8}{71}

Solution

More Steps

Evaluate

3 - \frac{8}{71}

An odd root of a negative radicand is always a negative

- 3 \frac{8}{71}

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

- \frac{3 8}{3 71}

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 71}

Multiply by the Conjugate

\frac{- 2 3 7 1 ^{2}}{3 71 \times 3 7 1 ^{2}}

Simplify

\frac{- 2 3 5041}{3 71 \times 3 7 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

371 \times 3 7 1^{2}

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

3 71 \times 7 1^{2}

Calculate the product

3 7 1^{3}

Reduce the index of the radical and exponent with 3

71

\frac{- 2 3 5041}{71}

Calculate

- \frac{2 3 5041}{71}

x = - \frac{2 3 5041}{71}

Alternative Form

x \approx - 0.482996

Show Solution