Solve x^3 -4x^25x-2

Question

Simplify the expression

- 19 x^{3} - 2

Evaluate

x^{3} - 4 x^{2} \times 5 x - 2

Multiply

More Steps

Multiply the terms

- 4 x^{2} \times 5 x

Multiply the terms

- 20 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 20 x^{2 + 1}

Add the numbers

- 20 x^{3}

x^{3} - 20 x^{3} - 2

Solution

More Steps

Evaluate

x^{3} - 20 x^{3}

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

(1 - 20) x^{3}

Subtract the numbers

- 19 x^{3}

- 19 x^{3} - 2

Show Solution

Find the roots

x = - \frac{3 722}{19}

Alternative Form

x \approx - 0.472163

Evaluate

x^{3} - 4 x^{2} \times 5 x - 2

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

x^{3} - 4 x^{2} \times 5 x - 2 = 0

Multiply

More Steps

Multiply the terms

4 x^{2} \times 5 x

Multiply the terms

20 x^{2} \times x

Multiply the terms with the same base by adding their exponents

20 x^{2 + 1}

Add the numbers

20 x^{3}

x^{3} - 20 x^{3} - 2 = 0

Subtract the terms

More Steps

Simplify

x^{3} - 20 x^{3}

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

(1 - 20) x^{3}

Subtract the numbers

- 19 x^{3}

- 19 x^{3} - 2 = 0

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

- 19 x^{3} = 0 + 2

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

- 19 x^{3} = 2

Change the signs on both sides of the equation

19 x^{3} = - 2

Divide both sides

\frac{19 x ^{3}}{19} = \frac{- 2}{19}

Divide the numbers

x^{3} = \frac{- 2}{19}

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

x^{3} = - \frac{2}{19}

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

3 x^{3} = 3 - \frac{2}{19}

Calculate

x = 3 - \frac{2}{19}

Solution

More Steps

Evaluate

3 - \frac{2}{19}

An odd root of a negative radicand is always a negative

- 3 \frac{2}{19}

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

- \frac{3 2}{3 19}

Multiply by the Conjugate

\frac{- 3 2 \times 3 1 9 ^{2}}{3 19 \times 3 1 9 ^{2}}

Simplify

\frac{- 3 2 \times 3 361}{3 19 \times 3 1 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 32 \times 3361

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

- 3 2 \times 361

Calculate the product

- 3722

\frac{- 3 722}{3 19 \times 3 1 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

319 \times 3 1 9^{2}

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

3 19 \times 1 9^{2}

Calculate the product

3 1 9^{3}

Reduce the index of the radical and exponent with 3

19

\frac{- 3 722}{19}

Calculate

- \frac{3 722}{19}

x = - \frac{3 722}{19}

Alternative Form

x \approx - 0.472163

Show Solution