Solve x^3-4x^23x-3=0

Question

Solve the equation

x = - \frac{3 363}{11}

Alternative Form

x \approx - 0.648499

Evaluate

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

Simplify

More Steps

Evaluate

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

Multiply

More Steps

Multiply the terms

- 4 x^{2} \times 3 x

Multiply the terms

- 12 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 12 x^{2 + 1}

Add the numbers

- 12 x^{3}

x^{3} - 12 x^{3} - 3

Subtract the terms

More Steps

Evaluate

x^{3} - 12 x^{3}

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

(1 - 12) x^{3}

Subtract the numbers

- 11 x^{3}

- 11 x^{3} - 3

- 11 x^{3} - 3 = 0

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

- 11 x^{3} = 0 + 3

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

- 11 x^{3} = 3

Change the signs on both sides of the equation

11 x^{3} = - 3

Divide both sides

\frac{11 x ^{3}}{11} = \frac{- 3}{11}

Divide the numbers

x^{3} = \frac{- 3}{11}

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

x^{3} = - \frac{3}{11}

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

3 x^{3} = 3 - \frac{3}{11}

Calculate

x = 3 - \frac{3}{11}

Solution

More Steps

Evaluate

3 - \frac{3}{11}

An odd root of a negative radicand is always a negative

- 3 \frac{3}{11}

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

- \frac{3 3}{3 11}

Multiply by the Conjugate

\frac{- 3 3 \times 3 1 1 ^{2}}{3 11 \times 3 1 1 ^{2}}

Simplify

\frac{- 3 3 \times 3 121}{3 11 \times 3 1 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 33 \times 3121

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

- 3 3 \times 121

Calculate the product

- 3363

\frac{- 3 363}{3 11 \times 3 1 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

311 \times 3 1 1^{2}

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

3 11 \times 1 1^{2}

Calculate the product

3 1 1^{3}

Reduce the index of the radical and exponent with 3

11

\frac{- 3 363}{11}

Calculate

- \frac{3 363}{11}

x = - \frac{3 363}{11}

Alternative Form

x \approx - 0.648499

Show Solution