Solve 4x-4⋅|-x^5| 5

Question

Simplify the expression

4 x - 20 x^{5}

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4 (x - 5 x^{5})

Show Solution

x_{1} = 0, x_{2} = \frac{4 125}{5}

Alternative Form

x_{1} = 0, x_{2} \approx 0.66874

Evaluate

4 x - 4 - x^{5} \times 5

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

4 x - 4 - x^{5} \times 5 = 0

Calculate the absolute value

4 x - 4 x^{5} \times 5 = 0

Multiply the terms

4 x - 20 x^{5} = 0

Separate the equation into 2 possible cases

4 x - 20 x^{5} = 0, x^{5} \geq 0 4 x - 20 (- x^{5}) = 0, x^{5} < 0

Solve the equation

More Steps

x = 0 x = \frac{4 125}{5} x = - \frac{4 125}{5}, x^{5} \geq 0 4 x - 20 (- x^{5}) = 0, x^{5} < 0

The only way a base raised to an odd power can be greater than or equal to 0 is if the base is greater than or equal to 0

x = 0 x = \frac{4 125}{5} x = - \frac{4 125}{5}, x \geq 0 4 x - 20 (- x^{5}) = 0, x^{5} < 0

Solve the equation

More Steps

x = 0 x = \frac{4 125}{5} x = - \frac{4 125}{5}, x \geq 0 x = 0 x = \frac{4 500}{10} - \frac{4 500}{10} i x = - \frac{4 500}{10} + \frac{4 500}{10} i, x^{5} < 0

The only way a base raised to an odd power can be less than 0 is if the base is less than 0

x = 0 x = \frac{4 125}{5} x = - \frac{4 125}{5}, x \geq 0 x = 0 x = \frac{4 500}{10} - \frac{4 500}{10} i x = - \frac{4 500}{10} + \frac{4 500}{10} i, x < 0

Find the intersection

x = 0 x = \frac{4 125}{5} x = 0 x = \frac{4 500}{10} - \frac{4 500}{10} i x = - \frac{4 500}{10} + \frac{4 500}{10} i, x < 0

Find the intersection

x = 0 x = \frac{4 125}{5} x \in \emptyset

Find the union

x = 0 x = \frac{4 125}{5}

Solution

x_{1} = 0, x_{2} = \frac{4 125}{5}

Alternative Form

x_{1} = 0, x_{2} \approx 0.66874

Show Solution