Solve x^3 - 4x^27x - 28

Question

Simplify the expression

- 27 x^{3} - 28

Evaluate

x^{3} - 4 x^{2} \times 7 x - 28

Multiply

More Steps

Multiply the terms

- 4 x^{2} \times 7 x

Multiply the terms

- 28 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 28 x^{2 + 1}

Add the numbers

- 28 x^{3}

x^{3} - 28 x^{3} - 28

Solution

More Steps

Evaluate

x^{3} - 28 x^{3}

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

(1 - 28) x^{3}

Subtract the numbers

- 27 x^{3}

- 27 x^{3} - 28

Show Solution

x = - \frac{3 28}{3}

Alternative Form

x \approx - 1.012196

Evaluate

x^{3} - 4 x^{2} \times 7 x - 28

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

x^{3} - 4 x^{2} \times 7 x - 28 = 0

Multiply

More Steps

Multiply the terms

4 x^{2} \times 7 x

Multiply the terms

28 x^{2} \times x

Multiply the terms with the same base by adding their exponents

28 x^{2 + 1}

Add the numbers

28 x^{3}

x^{3} - 28 x^{3} - 28 = 0

Subtract the terms

More Steps

Simplify

x^{3} - 28 x^{3}

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

(1 - 28) x^{3}

Subtract the numbers

- 27 x^{3}

- 27 x^{3} - 28 = 0

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

- 27 x^{3} = 0 + 28

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

- 27 x^{3} = 28

Change the signs on both sides of the equation

27 x^{3} = - 28

Divide both sides

\frac{27 x ^{3}}{27} = \frac{- 28}{27}

Divide the numbers

x^{3} = \frac{- 28}{27}

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

x^{3} = - \frac{28}{27}

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

3 x^{3} = 3 - \frac{28}{27}

Calculate

x = 3 - \frac{28}{27}

Solution

More Steps

Evaluate

3 - \frac{28}{27}

An odd root of a negative radicand is always a negative

- 3 \frac{28}{27}

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

- \frac{3 28}{3 27}

Simplify the radical expression

More Steps

Evaluate

327

Write the number in exponential form with the base of 3

3 3^{3}

Reduce the index of the radical and exponent with 3

3

- \frac{3 28}{3}

x = - \frac{3 28}{3}

Alternative Form

x \approx - 1.012196

Show Solution