Solve (x^5)/2-4x/3

Question

Simplify the expression

\frac{3 x ^{5} - 8 x}{6}

Evaluate

\frac{x ^{5}}{2} - (4 \times \frac{x}{3})

Multiply the terms

\frac{x ^{5}}{2} - \frac{4 x}{3}

Reduce fractions to a common denominator

\frac{x ^{5} \times 3}{2 \times 3} - \frac{4 x \times 2}{3 \times 2}

Multiply the numbers

\frac{x ^{5} \times 3}{6} - \frac{4 x \times 2}{3 \times 2}

Multiply the numbers

\frac{x ^{5} \times 3}{6} - \frac{4 x \times 2}{6}

Write all numerators above the common denominator

\frac{x ^{5} \times 3 - 4 x \times 2}{6}

Use the commutative property to reorder the terms

\frac{3 x ^{5} - 4 x \times 2}{6}

Solution

\frac{3 x ^{5} - 8 x}{6}

Show Solution

x_{1} = - \frac{4 216}{3}, x_{2} = 0, x_{3} = \frac{4 216}{3}

Alternative Form

x_{1} \approx - 1.277886, x_{2} = 0, x_{3} \approx 1.277886

Evaluate

\frac{x ^{5}}{2} - (4 \times \frac{x}{3})

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

\frac{x ^{5}}{2} - (4 \times \frac{x}{3}) = 0

Multiply the terms

\frac{x ^{5}}{2} - \frac{4 x}{3} = 0

Subtract the terms

More Steps

Simplify

\frac{x ^{5}}{2} - \frac{4 x}{3}

Reduce fractions to a common denominator

\frac{x ^{5} \times 3}{2 \times 3} - \frac{4 x \times 2}{3 \times 2}

Multiply the numbers

\frac{x ^{5} \times 3}{6} - \frac{4 x \times 2}{3 \times 2}

Multiply the numbers

\frac{x ^{5} \times 3}{6} - \frac{4 x \times 2}{6}

Write all numerators above the common denominator

\frac{x ^{5} \times 3 - 4 x \times 2}{6}

Use the commutative property to reorder the terms

\frac{3 x ^{5} - 4 x \times 2}{6}

Multiply the terms

\frac{3 x ^{5} - 8 x}{6}

\frac{3 x ^{5} - 8 x}{6} = 0

Simplify

3 x^{5} - 8 x = 0

Factor the expression

x (3 x^{4} - 8) = 0

Separate the equation into 2 possible cases

x = 0 3 x^{4} - 8 = 0

Solve the equation

More Steps

Evaluate

3 x^{4} - 8 = 0

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

3 x^{4} = 0 + 8

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

3 x^{4} = 8

Divide both sides

\frac{3 x ^{4}}{3} = \frac{8}{3}

Divide the numbers

x^{4} = \frac{8}{3}

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

x = \pm 4 \frac{8}{3}

Simplify the expression

More Steps

Evaluate

4 \frac{8}{3}

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

\frac{4 8}{4 3}

Multiply by the Conjugate

\frac{4 8 \times 4 3 ^{3}}{4 3 \times 4 3 ^{3}}

Simplify

\frac{4 8 \times 4 27}{4 3 \times 4 3 ^{3}}

Multiply the numbers

\frac{4 216}{4 3 \times 4 3 ^{3}}

Multiply the numbers

\frac{4 216}{3}

x = \pm \frac{4 216}{3}

Separate the equation into 2 possible cases

x = \frac{4 216}{3} x = - \frac{4 216}{3}

x = 0 x = \frac{4 216}{3} x = - \frac{4 216}{3}

Solution

x_{1} = - \frac{4 216}{3}, x_{2} = 0, x_{3} = \frac{4 216}{3}

Alternative Form

x_{1} \approx - 1.277886, x_{2} = 0, x_{3} \approx 1.277886

Show Solution