Solve -5x^2 6x - 6

Question

Simplify the expression

- 30 x^{3} - 6

Evaluate

- 5 x^{2} \times 6 x - 6

Solution

More Steps

Evaluate

- 5 x^{2} \times 6 x

Multiply the terms

- 30 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 30 x^{2 + 1}

Add the numbers

- 30 x^{3}

- 30 x^{3} - 6

Show Solution

Factor the expression

- 6 (5 x^{3} + 1)

Evaluate

- 5 x^{2} \times 6 x - 6

Multiply

More Steps

Evaluate

- 5 x^{2} \times 6 x

Multiply the terms

- 30 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 30 x^{2 + 1}

Add the numbers

- 30 x^{3}

- 30 x^{3} - 6

Solution

- 6 (5 x^{3} + 1)

Show Solution

Find the roots

x = - \frac{3 25}{5}

Alternative Form

x \approx - 0.584804

Evaluate

- 5 x^{2} \times 6 x - 6

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

- 5 x^{2} \times 6 x - 6 = 0

Multiply

More Steps

Multiply the terms

- 5 x^{2} \times 6 x

Multiply the terms

- 30 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 30 x^{2 + 1}

Add the numbers

- 30 x^{3}

- 30 x^{3} - 6 = 0

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

- 30 x^{3} = 0 + 6

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

- 30 x^{3} = 6

Change the signs on both sides of the equation

30 x^{3} = - 6

Divide both sides

\frac{30 x ^{3}}{30} = \frac{- 6}{30}

Divide the numbers

x^{3} = \frac{- 6}{30}

Divide the numbers

More Steps

Evaluate

\frac{- 6}{30}

Cancel out the common factor 6

\frac{- 1}{5}

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

- \frac{1}{5}

x^{3} = - \frac{1}{5}

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

3 x^{3} = 3 - \frac{1}{5}

Calculate

x = 3 - \frac{1}{5}

Solution

More Steps

Evaluate

3 - \frac{1}{5}

An odd root of a negative radicand is always a negative

- 3 \frac{1}{5}

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

- \frac{3 1}{3 5}

Simplify the radical expression

- \frac{1}{3 5}

Multiply by the Conjugate

\frac{- 3 5 ^{2}}{3 5 \times 3 5 ^{2}}

Simplify

\frac{- 3 25}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 3 5^{2}

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

3 5 \times 5^{2}

Calculate the product

3 5^{3}

Reduce the index of the radical and exponent with 3

5

\frac{- 3 25}{5}

Calculate

- \frac{3 25}{5}

x = - \frac{3 25}{5}

Alternative Form

x \approx - 0.584804

Show Solution