Solve (x^3 - 4x^2 x - 4)

Question

Simplify the expression

- 3 x^{3} - 4

Evaluate

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

Multiply

More Steps

Multiply the terms

- 4 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 4 x^{2 + 1}

Add the numbers

- 4 x^{3}

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

Solution

More Steps

Evaluate

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

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

(1 - 4) x^{3}

Subtract the numbers

- 3 x^{3}

- 3 x^{3} - 4

Show Solution

Find the roots

x = - \frac{3 36}{3}

Alternative Form

x \approx - 1.100642

Evaluate

(x^{3} - 4 x^{2} \times x - 4)

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

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

Multiply

More Steps

Multiply the terms

4 x^{2} \times x

Multiply the terms with the same base by adding their exponents

4 x^{2 + 1}

Add the numbers

4 x^{3}

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

Subtract the terms

More Steps

Simplify

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

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

(1 - 4) x^{3}

Subtract the numbers

- 3 x^{3}

- 3 x^{3} - 4 = 0

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

- 3 x^{3} = 0 + 4

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

- 3 x^{3} = 4

Change the signs on both sides of the equation

3 x^{3} = - 4

Divide both sides

\frac{3 x ^{3}}{3} = \frac{- 4}{3}

Divide the numbers

x^{3} = \frac{- 4}{3}

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

x^{3} = - \frac{4}{3}

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

3 x^{3} = 3 - \frac{4}{3}

Calculate

x = 3 - \frac{4}{3}

Solution

More Steps

Evaluate

3 - \frac{4}{3}

An odd root of a negative radicand is always a negative

- 3 \frac{4}{3}

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

- \frac{3 4}{3 3}

Multiply by the Conjugate

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

Simplify

\frac{- 3 4 \times 3 9}{3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 34 \times 39

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

- 3 4 \times 9

Calculate the product

- 336

\frac{- 3 36}{3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 3 3^{2}

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

3 3 \times 3^{2}

Calculate the product

3 3^{3}

Reduce the index of the radical and exponent with 3

3

\frac{- 3 36}{3}

Calculate

- \frac{3 36}{3}

x = - \frac{3 36}{3}

Alternative Form

x \approx - 1.100642

Show Solution