U(x)=x^5-8x^3+16x

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Solution for U(x)=x^5-8x^3+16x equation:


Simplifying
U(x) = x5 + -8x3 + 16x

Multiply U * x
xU = x5 + -8x3 + 16x

Reorder the terms:
xU = 16x + -8x3 + x5

Solving
xU = 16x + -8x3 + x5

Solving for variable 'x'.

Reorder the terms:
-16x + xU + 8x3 + -1x5 = 16x + -8x3 + x5 + -16x + 8x3 + -1x5

Reorder the terms:
-16x + xU + 8x3 + -1x5 = 16x + -16x + -8x3 + 8x3 + x5 + -1x5

Combine like terms: 16x + -16x = 0
-16x + xU + 8x3 + -1x5 = 0 + -8x3 + 8x3 + x5 + -1x5
-16x + xU + 8x3 + -1x5 = -8x3 + 8x3 + x5 + -1x5

Combine like terms: -8x3 + 8x3 = 0
-16x + xU + 8x3 + -1x5 = 0 + x5 + -1x5
-16x + xU + 8x3 + -1x5 = x5 + -1x5

Combine like terms: x5 + -1x5 = 0
-16x + xU + 8x3 + -1x5 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-16 + U + 8x2 + -1x4) = 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 '(-16 + U + 8x2 + -1x4)' equal to zero and attempt to solve: Simplifying -16 + U + 8x2 + -1x4 = 0 Solving -16 + U + 8x2 + -1x4 = 0 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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