Solve x^3-x^2 3x-3

Question

Simplify the expression

- 2 x^{3} - 3

Evaluate

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

Multiply

More Steps

Multiply the terms

- x^{2} \times 3 x

Multiply the terms with the same base by adding their exponents

- x^{2 + 1} \times 3

Add the numbers

- x^{3} \times 3

Use the commutative property to reorder the terms

- 3 x^{3}

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

Solution

More Steps

Evaluate

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

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

(1 - 3) x^{3}

Subtract the numbers

- 2 x^{3}

- 2 x^{3} - 3

Show Solution

Find the roots

x = - \frac{3 12}{2}

Alternative Form

x \approx - 1.144714

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

x^{2} \times 3 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 3

Add the numbers

x^{3} \times 3

Use the commutative property to reorder the terms

3 x^{3}

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

Subtract the terms

More Steps

Simplify

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

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

(1 - 3) x^{3}

Subtract the numbers

- 2 x^{3}

- 2 x^{3} - 3 = 0

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

- 2 x^{3} = 0 + 3

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

- 2 x^{3} = 3

Change the signs on both sides of the equation

2 x^{3} = - 3

Divide both sides

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

Divide the numbers

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

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

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

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

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

Calculate

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

Solution

More Steps

Evaluate

3 - \frac{3}{2}

An odd root of a negative radicand is always a negative

- 3 \frac{3}{2}

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

- \frac{3 3}{3 2}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

More Steps

Evaluate

- 33 \times 34

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

- 3 3 \times 4

Calculate the product

- 312

\frac{- 3 12}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

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

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{- 3 12}{2}

Calculate

- \frac{3 12}{2}

x = - \frac{3 12}{2}

Alternative Form

x \approx - 1.144714

Show Solution