Solve 3/8-16x^3 - ScanMath

Question

Factor the expression

\frac{1}{8} (3 - 128 x^{3})

Evaluate

\frac{3}{8} - 16 x^{3}

Solution

\frac{1}{8} (3 - 128 x^{3})

Show Solution

x = \frac{3 12}{8}

Alternative Form

x \approx 0.286179

Evaluate

\frac{3}{8} - 16 x^{3}

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

\frac{3}{8} - 16 x^{3} = 0

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

- 16 x^{3} = 0 - \frac{3}{8}

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

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

Change the signs on both sides of the equation

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

Multiply by the reciprocal

16 x^{3} \times \frac{1}{16} = \frac{3}{8} \times \frac{1}{16}

Multiply

x^{3} = \frac{3}{8} \times \frac{1}{16}

Multiply

More Steps

Evaluate

\frac{3}{8} \times \frac{1}{16}

To multiply the fractions,multiply the numerators and denominators separately

\frac{3}{8 \times 16}

Multiply the numbers

\frac{3}{128}

x^{3} = \frac{3}{128}

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

3 x^{3} = 3 \frac{3}{128}

Calculate

x = 3 \frac{3}{128}

Solution

More Steps

Evaluate

3 \frac{3}{128}

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

\frac{3 3}{3 128}

Simplify the radical expression

More Steps

Evaluate

3128

Write the expression as a product where the root of one of the factors can be evaluated

3 64 \times 2

Write the number in exponential form with the base of 4

3 4^{3} \times 2

The root of a product is equal to the product of the roots of each factor

3 4^{3} \times 32

Reduce the index of the radical and exponent with 3

432

\frac{3 3}{4 3 2}

Multiply by the Conjugate

\frac{3 3 \times 3 2 ^{2}}{4 3 2 \times 3 2 ^{2}}

Simplify

\frac{3 3 \times 3 4}{4 3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 34

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

3 3 \times 4

Calculate the product

312

\frac{3 12}{4 3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

432 \times 3 2^{2}

Multiply the terms

4 \times 2

Multiply the terms

8

\frac{3 12}{8}

x = \frac{3 12}{8}

Alternative Form

x \approx 0.286179

Show Solution