Solve -4x^2 24x-36

Question

Simplify the expression

- 96 x^{3} - 36

Evaluate

- 4 x^{2} \times 24 x - 36

Solution

More Steps

Evaluate

- 4 x^{2} \times 24 x

Multiply the terms

- 96 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 96 x^{2 + 1}

Add the numbers

- 96 x^{3}

- 96 x^{3} - 36

Show Solution

Factor the expression

- 12 (8 x^{3} + 3)

Evaluate

- 4 x^{2} \times 24 x - 36

Multiply

More Steps

Evaluate

- 4 x^{2} \times 24 x

Multiply the terms

- 96 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 96 x^{2 + 1}

Add the numbers

- 96 x^{3}

- 96 x^{3} - 36

Solution

- 12 (8 x^{3} + 3)

Show Solution

Find the roots

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

Alternative Form

x \approx - 0.721125

Evaluate

- 4 x^{2} \times 24 x - 36

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

- 4 x^{2} \times 24 x - 36 = 0

Multiply

More Steps

Multiply the terms

- 4 x^{2} \times 24 x

Multiply the terms

- 96 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 96 x^{2 + 1}

Add the numbers

- 96 x^{3}

- 96 x^{3} - 36 = 0

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

- 96 x^{3} = 0 + 36

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

- 96 x^{3} = 36

Change the signs on both sides of the equation

96 x^{3} = - 36

Divide both sides

\frac{96 x ^{3}}{96} = \frac{- 36}{96}

Divide the numbers

x^{3} = \frac{- 36}{96}

Divide the numbers

More Steps

Evaluate

\frac{- 36}{96}

Cancel out the common factor 12

\frac{- 3}{8}

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

- \frac{3}{8}

x^{3} = - \frac{3}{8}

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

3 x^{3} = 3 - \frac{3}{8}

Calculate

x = 3 - \frac{3}{8}

Solution

More Steps

Evaluate

3 - \frac{3}{8}

An odd root of a negative radicand is always a negative

- 3 \frac{3}{8}

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

- \frac{3 3}{3 8}

Simplify the radical expression

More Steps

Evaluate

38

Write the number in exponential form with the base of 2

3 2^{3}

Reduce the index of the radical and exponent with 3

2

- \frac{3 3}{2}

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

Alternative Form

x \approx - 0.721125

Show Solution