x^6=x

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Solution for x^6=x equation:


Simplifying
x6 = x

Solving
x6 = x

Solving for variable 'x'.

Reorder the terms:
-1x + x6 = x + -1x

Combine like terms: x + -1x = 0
-1x + x6 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + x5) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(-1 + x5)' equal to zero and attempt to solve: Simplifying -1 + x5 = 0 Solving -1 + x5 = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x5 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x5 = 0 + 1 x5 = 0 + 1 Combine like terms: 0 + 1 = 1 x5 = 1 Simplifying x5 = 1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

x = {0}

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