Solve 27x^(3)-512

Question

Factor the expression

(3 x - 8) (9 x^{2} + 24 x + 64)

Evaluate

27 x^{3} - 512

Rewrite the expression in exponential form

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

Use a^{3} - b^{3} = (a - b) (a^{2} + ab + b^{2}) to factor the expression

(3 x - 8) ((3 x)^{2} + 3 x \times 8 + 8^{2})

Evaluate

More Steps

Evaluate

(3 x)^{2}

To raise a product to a power,raise each factor to that power

3^{2} x^{2}

Evaluate the power

9 x^{2}

(3 x - 8) (9 x^{2} + 3 x \times 8 + 8^{2})

Evaluate

(3 x - 8) (9 x^{2} + 24 x + 8^{2})

Solution

(3 x - 8) (9 x^{2} + 24 x + 64)

Show Solution

x = \frac{8}{3}

Alternative Form

x = 2. \dot{6}

Evaluate

27 x^{3} - 512

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

27 x^{3} - 512 = 0

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

27 x^{3} = 0 + 512

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

27 x^{3} = 512

Divide both sides

\frac{27 x ^{3}}{27} = \frac{512}{27}

Divide the numbers

x^{3} = \frac{512}{27}

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

3 x^{3} = 3 \frac{512}{27}

Calculate

x = 3 \frac{512}{27}

Solution

More Steps

Evaluate

3 \frac{512}{27}

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

\frac{3 512}{3 27}

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{8}{3 27}

Simplify the radical expression

More Steps

Evaluate

327

Write the number in exponential form with the base of 3

3 3^{3}

Reduce the index of the radical and exponent with 3

3

\frac{8}{3}

x = \frac{8}{3}

Alternative Form

x = 2. \dot{6}

Show Solution