Solve 8x^3 - 729 - ScanMath

Question

Factor the expression

(2 x - 9) (4 x^{2} + 18 x + 81)

Evaluate

8 x^{3} - 729

Rewrite the expression in exponential form

(2 x)^{3} - 9^{3}

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

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

Evaluate

More Steps

Evaluate

(2 x)^{2}

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

2^{2} x^{2}

Evaluate the power

4 x^{2}

(2 x - 9) (4 x^{2} + 2 x \times 9 + 9^{2})

Evaluate

(2 x - 9) (4 x^{2} + 18 x + 9^{2})

Solution

(2 x - 9) (4 x^{2} + 18 x + 81)

Show Solution

x = \frac{9}{2}

Alternative Form

x = 4.5

Evaluate

8 x^{3} - 729

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

8 x^{3} - 729 = 0

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

8 x^{3} = 0 + 729

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

8 x^{3} = 729

Divide both sides

\frac{8 x ^{3}}{8} = \frac{729}{8}

Divide the numbers

x^{3} = \frac{729}{8}

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

3 x^{3} = 3 \frac{729}{8}

Calculate

x = 3 \frac{729}{8}

Solution

More Steps

Evaluate

3 \frac{729}{8}

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

\frac{3 729}{3 8}

Simplify the radical expression

More Steps

Evaluate

3729

Write the number in exponential form with the base of 9

3 9^{3}

Reduce the index of the radical and exponent with 3

9

\frac{9}{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{9}{2}

x = \frac{9}{2}

Alternative Form

x = 4.5

Show Solution