Solve x^7/7-x^4/2 x

Question

Simplify the expression

\frac{2 x ^{7} - 7 x ^{5}}{14}

Show Solution

x_{1} = - \frac{14}{2}, x_{2} = 0, x_{3} = \frac{14}{2}

Alternative Form

x_{1} \approx - 1.870829, x_{2} = 0, x_{3} \approx 1.870829

Evaluate

\frac{x ^{7}}{7} - \frac{x ^{4}}{2} x

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

\frac{x ^{7}}{7} - \frac{x ^{4}}{2} x = 0

Multiply the terms

More Steps

\frac{x ^{7}}{7} - \frac{x ^{5}}{2} = 0

Subtract the terms

More Steps

\frac{2 x ^{7} - 7 x ^{5}}{14} = 0

Simplify

2 x^{7} - 7 x^{5} = 0

Factor the expression

x^{5} (2 x^{2} - 7) = 0

Separate the equation into 2 possible cases

x^{5} = 0 2 x^{2} - 7 = 0

The only way a power can be 0 is when the base equals 0

x = 0 2 x^{2} - 7 = 0

Solve the equation

More Steps

x = 0 x = \frac{14}{2} x = - \frac{14}{2}

Solution

x_{1} = - \frac{14}{2}, x_{2} = 0, x_{3} = \frac{14}{2}

Alternative Form

x_{1} \approx - 1.870829, x_{2} = 0, x_{3} \approx 1.870829

Show Solution