Solve 4x - 5x^7/8

Question

Simplify the expression

\frac{32 x - 5 x ^{7}}{8}

Evaluate

4 x - (5 \times \frac{x ^{7}}{8})

Multiply the terms

4 x - \frac{5 x ^{7}}{8}

Reduce fractions to a common denominator

\frac{4 x \times 8}{8} - \frac{5 x ^{7}}{8}

Write all numerators above the common denominator

\frac{4 x \times 8 - 5 x ^{7}}{8}

Solution

\frac{32 x - 5 x ^{7}}{8}

Show Solution

x_{1} = - \frac{6 100000}{5}, x_{2} = 0, x_{3} = \frac{6 100000}{5}

Alternative Form

x_{1} \approx - 1.362584, x_{2} = 0, x_{3} \approx 1.362584

Evaluate

4 x - (5 \times \frac{x ^{7}}{8})

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

4 x - (5 \times \frac{x ^{7}}{8}) = 0

Multiply the terms

4 x - \frac{5 x ^{7}}{8} = 0

Subtract the terms

More Steps

Simplify

4 x - \frac{5 x ^{7}}{8}

Reduce fractions to a common denominator

\frac{4 x \times 8}{8} - \frac{5 x ^{7}}{8}

Write all numerators above the common denominator

\frac{4 x \times 8 - 5 x ^{7}}{8}

Multiply the terms

\frac{32 x - 5 x ^{7}}{8}

\frac{32 x - 5 x ^{7}}{8} = 0

Simplify

32 x - 5 x^{7} = 0

Factor the expression

x (32 - 5 x^{6}) = 0

Separate the equation into 2 possible cases

x = 0 32 - 5 x^{6} = 0

Solve the equation

More Steps

Evaluate

32 - 5 x^{6} = 0

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

- 5 x^{6} = 0 - 32

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

- 5 x^{6} = - 32

Change the signs on both sides of the equation

5 x^{6} = 32

Divide both sides

\frac{5 x ^{6}}{5} = \frac{32}{5}

Divide the numbers

x^{6} = \frac{32}{5}

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

x = \pm 6 \frac{32}{5}

Simplify the expression

More Steps

Evaluate

6 \frac{32}{5}

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

\frac{6 32}{6 5}

Multiply by the Conjugate

\frac{6 32 \times 6 5 ^{5}}{6 5 \times 6 5 ^{5}}

Simplify

\frac{6 32 \times 6 3125}{6 5 \times 6 5 ^{5}}

Multiply the numbers

\frac{6 100000}{6 5 \times 6 5 ^{5}}

Multiply the numbers

\frac{6 100000}{5}

x = \pm \frac{6 100000}{5}

Separate the equation into 2 possible cases

x = \frac{6 100000}{5} x = - \frac{6 100000}{5}

x = 0 x = \frac{6 100000}{5} x = - \frac{6 100000}{5}

Solution

x_{1} = - \frac{6 100000}{5}, x_{2} = 0, x_{3} = \frac{6 100000}{5}

Alternative Form

x_{1} \approx - 1.362584, x_{2} = 0, x_{3} \approx 1.362584

Show Solution