Solve 4x^3-12x^2 9x-2

Question

Simplify the expression

- 104 x^{3} - 2

Evaluate

4 x^{3} - 12 x^{2} \times 9 x - 2

Multiply

More Steps

Multiply the terms

- 12 x^{2} \times 9 x

Multiply the terms

- 108 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 108 x^{2 + 1}

Add the numbers

- 108 x^{3}

4 x^{3} - 108 x^{3} - 2

Solution

More Steps

Evaluate

4 x^{3} - 108 x^{3}

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

(4 - 108) x^{3}

Subtract the numbers

- 104 x^{3}

- 104 x^{3} - 2

Show Solution

Factor the expression

- 2 (52 x^{3} + 1)

Evaluate

4 x^{3} - 12 x^{2} \times 9 x - 2

Multiply

More Steps

Multiply the terms

12 x^{2} \times 9 x

Multiply the terms

108 x^{2} \times x

Multiply the terms with the same base by adding their exponents

108 x^{2 + 1}

Add the numbers

108 x^{3}

4 x^{3} - 108 x^{3} - 2

Subtract the terms

More Steps

Simplify

4 x^{3} - 108 x^{3}

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

(4 - 108) x^{3}

Subtract the numbers

- 104 x^{3}

- 104 x^{3} - 2

Solution

- 2 (52 x^{3} + 1)

Show Solution

Find the roots

x = - \frac{3 338}{26}

Alternative Form

x \approx - 0.267916

Evaluate

4 x^{3} - 12 x^{2} \times 9 x - 2

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

4 x^{3} - 12 x^{2} \times 9 x - 2 = 0

Multiply

More Steps

Multiply the terms

12 x^{2} \times 9 x

Multiply the terms

108 x^{2} \times x

Multiply the terms with the same base by adding their exponents

108 x^{2 + 1}

Add the numbers

108 x^{3}

4 x^{3} - 108 x^{3} - 2 = 0

Subtract the terms

More Steps

Simplify

4 x^{3} - 108 x^{3}

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

(4 - 108) x^{3}

Subtract the numbers

- 104 x^{3}

- 104 x^{3} - 2 = 0

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

- 104 x^{3} = 0 + 2

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

- 104 x^{3} = 2

Change the signs on both sides of the equation

104 x^{3} = - 2

Divide both sides

\frac{104 x ^{3}}{104} = \frac{- 2}{104}

Divide the numbers

x^{3} = \frac{- 2}{104}

Divide the numbers

More Steps

Evaluate

\frac{- 2}{104}

Cancel out the common factor 2

\frac{- 1}{52}

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

- \frac{1}{52}

x^{3} = - \frac{1}{52}

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

3 x^{3} = 3 - \frac{1}{52}

Calculate

x = 3 - \frac{1}{52}

Solution

More Steps

Evaluate

3 - \frac{1}{52}

An odd root of a negative radicand is always a negative

- 3 \frac{1}{52}

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

- \frac{3 1}{3 52}

Simplify the radical expression

- \frac{1}{3 52}

Multiply by the Conjugate

\frac{- 3 5 2 ^{2}}{3 52 \times 3 5 2 ^{2}}

Simplify

\frac{- 2 3 338}{3 52 \times 3 5 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

352 \times 3 5 2^{2}

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

3 52 \times 5 2^{2}

Calculate the product

3 5 2^{3}

Reduce the index of the radical and exponent with 3

52

\frac{- 2 3 338}{52}

Cancel out the common factor 2

\frac{- 3 338}{26}

Calculate

- \frac{3 338}{26}

x = - \frac{3 338}{26}

Alternative Form

x \approx - 0.267916

Show Solution