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

Question

Simplify the expression

- 36 x^{3} - 12

Evaluate

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

Solution

More Steps

Evaluate

- 3 x^{2} \times 12 x

Multiply the terms

- 36 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 36 x^{2 + 1}

Add the numbers

- 36 x^{3}

- 36 x^{3} - 12

Show Solution

Factor the expression

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

Evaluate

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

Multiply

More Steps

Evaluate

- 3 x^{2} \times 12 x

Multiply the terms

- 36 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 36 x^{2 + 1}

Add the numbers

- 36 x^{3}

- 36 x^{3} - 12

Solution

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

Show Solution

Find the roots

x = - \frac{3 9}{3}

Alternative Form

x \approx - 0.693361

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

- 3 x^{2} \times 12 x

Multiply the terms

- 36 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 36 x^{2 + 1}

Add the numbers

- 36 x^{3}

- 36 x^{3} - 12 = 0

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

- 36 x^{3} = 0 + 12

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

- 36 x^{3} = 12

Change the signs on both sides of the equation

36 x^{3} = - 12

Divide both sides

\frac{36 x ^{3}}{36} = \frac{- 12}{36}

Divide the numbers

x^{3} = \frac{- 12}{36}

Divide the numbers

More Steps

Evaluate

\frac{- 12}{36}

Cancel out the common factor 12

\frac{- 1}{3}

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

- \frac{1}{3}

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

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

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

Calculate

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

Solution

More Steps

Evaluate

3 - \frac{1}{3}

An odd root of a negative radicand is always a negative

- 3 \frac{1}{3}

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

- \frac{3 1}{3 3}

Simplify the radical expression

- \frac{1}{3 3}

Multiply by the Conjugate

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

Simplify

\frac{- 3 9}{3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 3 3^{2}

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

3 3 \times 3^{2}

Calculate the product

3 3^{3}

Reduce the index of the radical and exponent with 3

3

\frac{- 3 9}{3}

Calculate

- \frac{3 9}{3}

x = - \frac{3 9}{3}

Alternative Form

x \approx - 0.693361

Show Solution