Solve 2x^3-6x^26x-1

Question

Simplify the expression

- 34 x^{3} - 1

Evaluate

2 x^{3} - 6 x^{2} \times 6 x - 1

Multiply

More Steps

Multiply the terms

- 6 x^{2} \times 6 x

Multiply the terms

- 36 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 36 x^{2 + 1}

Add the numbers

- 36 x^{3}

2 x^{3} - 36 x^{3} - 1

Solution

More Steps

Evaluate

2 x^{3} - 36 x^{3}

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

(2 - 36) x^{3}

Subtract the numbers

- 34 x^{3}

- 34 x^{3} - 1

Show Solution

Find the roots

x = - \frac{3 1156}{34}

Alternative Form

x \approx - 0.308679

Evaluate

2 x^{3} - 6 x^{2} \times 6 x - 1

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

2 x^{3} - 6 x^{2} \times 6 x - 1 = 0

Multiply

More Steps

Multiply the terms

6 x^{2} \times 6 x

Multiply the terms

36 x^{2} \times x

Multiply the terms with the same base by adding their exponents

36 x^{2 + 1}

Add the numbers

36 x^{3}

2 x^{3} - 36 x^{3} - 1 = 0

Subtract the terms

More Steps

Simplify

2 x^{3} - 36 x^{3}

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

(2 - 36) x^{3}

Subtract the numbers

- 34 x^{3}

- 34 x^{3} - 1 = 0

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

- 34 x^{3} = 0 + 1

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

- 34 x^{3} = 1

Change the signs on both sides of the equation

34 x^{3} = - 1

Divide both sides

\frac{34 x ^{3}}{34} = \frac{- 1}{34}

Divide the numbers

x^{3} = \frac{- 1}{34}

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

x^{3} = - \frac{1}{34}

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

3 x^{3} = 3 - \frac{1}{34}

Calculate

x = 3 - \frac{1}{34}

Solution

More Steps

Evaluate

3 - \frac{1}{34}

An odd root of a negative radicand is always a negative

- 3 \frac{1}{34}

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

- \frac{3 1}{3 34}

Simplify the radical expression

- \frac{1}{3 34}

Multiply by the Conjugate

\frac{- 3 3 4 ^{2}}{3 34 \times 3 3 4 ^{2}}

Simplify

\frac{- 3 1156}{3 34 \times 3 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

334 \times 3 3 4^{2}

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

3 34 \times 3 4^{2}

Calculate the product

3 3 4^{3}

Reduce the index of the radical and exponent with 3

34

\frac{- 3 1156}{34}

Calculate

- \frac{3 1156}{34}

x = - \frac{3 1156}{34}

Alternative Form

x \approx - 0.308679

Show Solution