z^5-25z=0

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Solution for z^5-25z=0 equation:


Simplifying
z5 + -25z = 0

Reorder the terms:
-25z + z5 = 0

Solving
-25z + z5 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(-25 + z4) = 0

Factor a difference between two squares.
z((5 + z2)(-5 + z2)) = 0

Subproblem 1

Set the factor 'z' equal to zero and attempt to solve: Simplifying z = 0 Solving z = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z = 0

Subproblem 2

Set the factor '(5 + z2)' equal to zero and attempt to solve: Simplifying 5 + z2 = 0 Solving 5 + z2 = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + z2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + z2 = 0 + -5 z2 = 0 + -5 Combine like terms: 0 + -5 = -5 z2 = -5 Simplifying z2 = -5 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 3

Set the factor '(-5 + z2)' equal to zero and attempt to solve: Simplifying -5 + z2 = 0 Solving -5 + z2 = 0 Move all terms containing z to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + z2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + z2 = 0 + 5 z2 = 0 + 5 Combine like terms: 0 + 5 = 5 z2 = 5 Simplifying z2 = 5 Take the square root of each side: z = {-2.236067978, 2.236067978}

Solution

z = {0, -2.236067978, 2.236067978}

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