Solve x^3-3x^29x-27

Question

Simplify the expression

- 26 x^{3} - 27

Evaluate

x^{3} - 3 x^{2} \times 9 x - 27

Multiply

More Steps

Multiply the terms

- 3 x^{2} \times 9 x

Multiply the terms

- 27 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 27 x^{2 + 1}

Add the numbers

- 27 x^{3}

x^{3} - 27 x^{3} - 27

Solution

More Steps

Evaluate

x^{3} - 27 x^{3}

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

(1 - 27) x^{3}

Subtract the numbers

- 26 x^{3}

- 26 x^{3} - 27

Show Solution

Find the roots

x = - \frac{3 3 676}{26}

Alternative Form

x \approx - 1.01266

Evaluate

x^{3} - 3 x^{2} \times 9 x - 27

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

x^{3} - 3 x^{2} \times 9 x - 27 = 0

Multiply

More Steps

Multiply the terms

3 x^{2} \times 9 x

Multiply the terms

27 x^{2} \times x

Multiply the terms with the same base by adding their exponents

27 x^{2 + 1}

Add the numbers

27 x^{3}

x^{3} - 27 x^{3} - 27 = 0

Subtract the terms

More Steps

Simplify

x^{3} - 27 x^{3}

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

(1 - 27) x^{3}

Subtract the numbers

- 26 x^{3}

- 26 x^{3} - 27 = 0

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

- 26 x^{3} = 0 + 27

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

- 26 x^{3} = 27

Change the signs on both sides of the equation

26 x^{3} = - 27

Divide both sides

\frac{26 x ^{3}}{26} = \frac{- 27}{26}

Divide the numbers

x^{3} = \frac{- 27}{26}

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

x^{3} = - \frac{27}{26}

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

3 x^{3} = 3 - \frac{27}{26}

Calculate

x = 3 - \frac{27}{26}

Solution

More Steps

Evaluate

3 - \frac{27}{26}

An odd root of a negative radicand is always a negative

- 3 \frac{27}{26}

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

- \frac{3 27}{3 26}

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}{3 26}

Multiply by the Conjugate

\frac{- 3 3 2 6 ^{2}}{3 26 \times 3 2 6 ^{2}}

Simplify

\frac{- 3 3 676}{3 26 \times 3 2 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

326 \times 3 2 6^{2}

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

3 26 \times 2 6^{2}

Calculate the product

3 2 6^{3}

Reduce the index of the radical and exponent with 3

26

\frac{- 3 3 676}{26}

Calculate

- \frac{3 3 676}{26}

x = - \frac{3 3 676}{26}

Alternative Form

x \approx - 1.01266

Show Solution