Solve 1x1-3/16x^3/32

Question

Simplify the expression

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

Evaluate

1 \times x \times 1 - \frac{3}{16} \times \frac{x ^{3}}{32}

Multiply the terms

x - \frac{3}{16} \times \frac{x ^{3}}{32}

Multiply the terms

More Steps

Evaluate

\frac{3}{16} \times \frac{x ^{3}}{32}

Multiply the terms

\frac{3 x ^{3}}{16 \times 32}

Multiply the terms

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

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

Reduce fractions to a common denominator

\frac{x \times 512}{512} - \frac{3 x ^{3}}{512}

Write all numerators above the common denominator

\frac{x \times 512 - 3 x ^{3}}{512}

Solution

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

Show Solution

Find the roots

x_{1} = - \frac{16 6}{3}, x_{2} = 0, x_{3} = \frac{16 6}{3}

Alternative Form

x_{1} \approx - 13.063945, x_{2} = 0, x_{3} \approx 13.063945

Evaluate

1 \times x \times 1 - \frac{3}{16} \times \frac{x ^{3}}{32}

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

1 \times x \times 1 - \frac{3}{16} \times \frac{x ^{3}}{32} = 0

Multiply the terms

x - \frac{3}{16} \times \frac{x ^{3}}{32} = 0

Multiply the terms

More Steps

Evaluate

\frac{3}{16} \times \frac{x ^{3}}{32}

Multiply the terms

\frac{3 x ^{3}}{16 \times 32}

Multiply the terms

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

x - \frac{3 x ^{3}}{512} = 0

Subtract the terms

More Steps

Simplify

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

Reduce fractions to a common denominator

\frac{x \times 512}{512} - \frac{3 x ^{3}}{512}

Write all numerators above the common denominator

\frac{x \times 512 - 3 x ^{3}}{512}

Use the commutative property to reorder the terms

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

\frac{512 x - 3 x ^{3}}{512} = 0

Simplify

512 x - 3 x^{3} = 0

Factor the expression

x (512 - 3 x^{2}) = 0

Separate the equation into 2 possible cases

x = 0 512 - 3 x^{2} = 0

Solve the equation

More Steps

Evaluate

512 - 3 x^{2} = 0

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

- 3 x^{2} = 0 - 512

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

- 3 x^{2} = - 512

Change the signs on both sides of the equation

3 x^{2} = 512

Divide both sides

\frac{3 x ^{2}}{3} = \frac{512}{3}

Divide the numbers

x^{2} = \frac{512}{3}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{512}{3}

Simplify the expression

More Steps

Evaluate

\frac{512}{3}

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

\frac{512}{3}

Simplify the radical expression

\frac{16 2}{3}

Multiply by the Conjugate

\frac{16 2 \times 3}{3 \times 3}

Multiply the numbers

\frac{16 6}{3 \times 3}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{16 6}{3}

x = \pm \frac{16 6}{3}

Separate the equation into 2 possible cases

x = \frac{16 6}{3} x = - \frac{16 6}{3}

x = 0 x = \frac{16 6}{3} x = - \frac{16 6}{3}

Solution

x_{1} = - \frac{16 6}{3}, x_{2} = 0, x_{3} = \frac{16 6}{3}

Alternative Form

x_{1} \approx - 13.063945, x_{2} = 0, x_{3} \approx 13.063945

Show Solution