Solve 4x^(3)-19x^(2) 4x-12

Question

Simplify the expression

- 72 x^{3} - 12

Evaluate

4 x^{3} - 19 x^{2} \times 4 x - 12

Multiply

More Steps

Multiply the terms

- 19 x^{2} \times 4 x

Multiply the terms

- 76 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 76 x^{2 + 1}

Add the numbers

- 76 x^{3}

4 x^{3} - 76 x^{3} - 12

Solution

More Steps

Evaluate

4 x^{3} - 76 x^{3}

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

(4 - 76) x^{3}

Subtract the numbers

- 72 x^{3}

- 72 x^{3} - 12

Show Solution

Factor the expression

- 12 (6 x^{3} + 1)

Evaluate

4 x^{3} - 19 x^{2} \times 4 x - 12

Multiply

More Steps

Multiply the terms

19 x^{2} \times 4 x

Multiply the terms

76 x^{2} \times x

Multiply the terms with the same base by adding their exponents

76 x^{2 + 1}

Add the numbers

76 x^{3}

4 x^{3} - 76 x^{3} - 12

Subtract the terms

More Steps

Simplify

4 x^{3} - 76 x^{3}

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

(4 - 76) x^{3}

Subtract the numbers

- 72 x^{3}

- 72 x^{3} - 12

Solution

- 12 (6 x^{3} + 1)

Show Solution

Find the roots

x = - \frac{3 36}{6}

Alternative Form

x \approx - 0.550321

Evaluate

4 x^{3} - 19 x^{2} \times 4 x - 12

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

4 x^{3} - 19 x^{2} \times 4 x - 12 = 0

Multiply

More Steps

Multiply the terms

19 x^{2} \times 4 x

Multiply the terms

76 x^{2} \times x

Multiply the terms with the same base by adding their exponents

76 x^{2 + 1}

Add the numbers

76 x^{3}

4 x^{3} - 76 x^{3} - 12 = 0

Subtract the terms

More Steps

Simplify

4 x^{3} - 76 x^{3}

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

(4 - 76) x^{3}

Subtract the numbers

- 72 x^{3}

- 72 x^{3} - 12 = 0

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

- 72 x^{3} = 0 + 12

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

- 72 x^{3} = 12

Change the signs on both sides of the equation

72 x^{3} = - 12

Divide both sides

\frac{72 x ^{3}}{72} = \frac{- 12}{72}

Divide the numbers

x^{3} = \frac{- 12}{72}

Divide the numbers

More Steps

Evaluate

\frac{- 12}{72}

Cancel out the common factor 12

\frac{- 1}{6}

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

- \frac{1}{6}

x^{3} = - \frac{1}{6}

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

3 x^{3} = 3 - \frac{1}{6}

Calculate

x = 3 - \frac{1}{6}

Solution

More Steps

Evaluate

3 - \frac{1}{6}

An odd root of a negative radicand is always a negative

- 3 \frac{1}{6}

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

- \frac{3 1}{3 6}

Simplify the radical expression

- \frac{1}{3 6}

Multiply by the Conjugate

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

Simplify

\frac{- 3 36}{3 6 \times 3 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

36 \times 3 6^{2}

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

3 6 \times 6^{2}

Calculate the product

3 6^{3}

Reduce the index of the radical and exponent with 3

6

\frac{- 3 36}{6}

Calculate

- \frac{3 36}{6}

x = - \frac{3 36}{6}

Alternative Form

x \approx - 0.550321

Show Solution