Solve 5x^3-10x^2 6x-12

Question

Simplify the expression

- 55 x^{3} - 12

Evaluate

5 x^{3} - 10 x^{2} \times 6 x - 12

Multiply

More Steps

Multiply the terms

- 10 x^{2} \times 6 x

Multiply the terms

- 60 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 60 x^{2 + 1}

Add the numbers

- 60 x^{3}

5 x^{3} - 60 x^{3} - 12

Solution

More Steps

Evaluate

5 x^{3} - 60 x^{3}

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

(5 - 60) x^{3}

Subtract the numbers

- 55 x^{3}

- 55 x^{3} - 12

Show Solution

Find the roots

x = - \frac{3 36300}{55}

Alternative Form

x \approx - 0.602013

Evaluate

5 x^{3} - 10 x^{2} \times 6 x - 12

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

5 x^{3} - 10 x^{2} \times 6 x - 12 = 0

Multiply

More Steps

Multiply the terms

10 x^{2} \times 6 x

Multiply the terms

60 x^{2} \times x

Multiply the terms with the same base by adding their exponents

60 x^{2 + 1}

Add the numbers

60 x^{3}

5 x^{3} - 60 x^{3} - 12 = 0

Subtract the terms

More Steps

Simplify

5 x^{3} - 60 x^{3}

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

(5 - 60) x^{3}

Subtract the numbers

- 55 x^{3}

- 55 x^{3} - 12 = 0

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

- 55 x^{3} = 0 + 12

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

- 55 x^{3} = 12

Change the signs on both sides of the equation

55 x^{3} = - 12

Divide both sides

\frac{55 x ^{3}}{55} = \frac{- 12}{55}

Divide the numbers

x^{3} = \frac{- 12}{55}

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

x^{3} = - \frac{12}{55}

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

3 x^{3} = 3 - \frac{12}{55}

Calculate

x = 3 - \frac{12}{55}

Solution

More Steps

Evaluate

3 - \frac{12}{55}

An odd root of a negative radicand is always a negative

- 3 \frac{12}{55}

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

- \frac{3 12}{3 55}

Multiply by the Conjugate

\frac{- 3 12 \times 3 5 5 ^{2}}{3 55 \times 3 5 5 ^{2}}

Simplify

\frac{- 3 12 \times 3 3025}{3 55 \times 3 5 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 312 \times 33025

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

- 3 12 \times 3025

Calculate the product

- 336300

\frac{- 3 36300}{3 55 \times 3 5 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

355 \times 3 5 5^{2}

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

3 55 \times 5 5^{2}

Calculate the product

3 5 5^{3}

Reduce the index of the radical and exponent with 3

55

\frac{- 3 36300}{55}

Calculate

- \frac{3 36300}{55}

x = - \frac{3 36300}{55}

Alternative Form

x \approx - 0.602013

Show Solution