Solve 64x^3-48x^2 12x-1

Question

Simplify the expression

- 512 x^{3} - 1

Evaluate

64 x^{3} - 48 x^{2} \times 12 x - 1

Multiply

More Steps

Multiply the terms

- 48 x^{2} \times 12 x

Multiply the terms

- 576 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 576 x^{2 + 1}

Add the numbers

- 576 x^{3}

64 x^{3} - 576 x^{3} - 1

Solution

More Steps

Evaluate

64 x^{3} - 576 x^{3}

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

(64 - 576) x^{3}

Subtract the numbers

- 512 x^{3}

- 512 x^{3} - 1

Show Solution

Factor the expression

- (8 x + 1) (64 x^{2} - 8 x + 1)

Evaluate

64 x^{3} - 48 x^{2} \times 12 x - 1

Multiply

More Steps

Multiply the terms

48 x^{2} \times 12 x

Multiply the terms

576 x^{2} \times x

Multiply the terms with the same base by adding their exponents

576 x^{2 + 1}

Add the numbers

576 x^{3}

64 x^{3} - 576 x^{3} - 1

Subtract the terms

More Steps

Simplify

64 x^{3} - 576 x^{3}

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

(64 - 576) x^{3}

Subtract the numbers

- 512 x^{3}

- 512 x^{3} - 1

Factor out - 1 from the expression

- (512 x^{3} + 1)

Solution

More Steps

Evaluate

512 x^{3} + 1

Calculate

512 x^{3} - 64 x^{2} + 8 x + 64 x^{2} - 8 x + 1

Rewrite the expression

8 x \times 64 x^{2} - 8 x \times 8 x + 8 x + 64 x^{2} - 8 x + 1

Factor out 8 x from the expression

8 x (64 x^{2} - 8 x + 1) + 64 x^{2} - 8 x + 1

Factor out 64 x^{2} - 8 x + 1 from the expression

(8 x + 1) (64 x^{2} - 8 x + 1)

- (8 x + 1) (64 x^{2} - 8 x + 1)

Show Solution

Find the roots

x = - \frac{1}{8}

Alternative Form

x = - 0.125

Evaluate

64 x^{3} - 48 x^{2} \times 12 x - 1

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

64 x^{3} - 48 x^{2} \times 12 x - 1 = 0

Multiply

More Steps

Multiply the terms

48 x^{2} \times 12 x

Multiply the terms

576 x^{2} \times x

Multiply the terms with the same base by adding their exponents

576 x^{2 + 1}

Add the numbers

576 x^{3}

64 x^{3} - 576 x^{3} - 1 = 0

Subtract the terms

More Steps

Simplify

64 x^{3} - 576 x^{3}

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

(64 - 576) x^{3}

Subtract the numbers

- 512 x^{3}

- 512 x^{3} - 1 = 0

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

- 512 x^{3} = 0 + 1

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

- 512 x^{3} = 1

Change the signs on both sides of the equation

512 x^{3} = - 1

Divide both sides

\frac{512 x ^{3}}{512} = \frac{- 1}{512}

Divide the numbers

x^{3} = \frac{- 1}{512}

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

x^{3} = - \frac{1}{512}

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

3 x^{3} = 3 - \frac{1}{512}

Calculate

x = 3 - \frac{1}{512}

Solution

More Steps

Evaluate

3 - \frac{1}{512}

An odd root of a negative radicand is always a negative

- 3 \frac{1}{512}

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

- \frac{3 1}{3 512}

Simplify the radical expression

- \frac{1}{3 512}

Simplify the radical expression

More Steps

Evaluate

3512

Write the number in exponential form with the base of 8

3 8^{3}

Reduce the index of the radical and exponent with 3

8

- \frac{1}{8}

x = - \frac{1}{8}

Alternative Form

x = - 0.125

Show Solution