0=x^5+x^3-6x

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Solution for 0=x^5+x^3-6x equation:


Simplifying
0 = x5 + x3 + -6x

Reorder the terms:
0 = -6x + x3 + x5

Solving
0 = -6x + x3 + x5

Solving for variable 'x'.
Remove the zero:
6x + -1x3 + -1x5 = -6x + x3 + x5 + 6x + -1x3 + -1x5

Reorder the terms:
6x + -1x3 + -1x5 = -6x + 6x + x3 + -1x3 + x5 + -1x5

Combine like terms: -6x + 6x = 0
6x + -1x3 + -1x5 = 0 + x3 + -1x3 + x5 + -1x5
6x + -1x3 + -1x5 = x3 + -1x3 + x5 + -1x5

Combine like terms: x3 + -1x3 = 0
6x + -1x3 + -1x5 = 0 + x5 + -1x5
6x + -1x3 + -1x5 = x5 + -1x5

Combine like terms: x5 + -1x5 = 0
6x + -1x3 + -1x5 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(6 + -1x2 + -1x4) = 0

Factor a trinomial.
x((2 + -1x2)(3 + x2)) = 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 '(2 + -1x2)' equal to zero and attempt to solve: Simplifying 2 + -1x2 = 0 Solving 2 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x2 = 0 + -2 -1x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1x2 = -2 Divide each side by '-1'. x2 = 2 Simplifying x2 = 2 Take the square root of each side: x = {-1.414213562, 1.414213562}

Subproblem 3

Set the factor '(3 + x2)' equal to zero and attempt to solve: Simplifying 3 + x2 = 0 Solving 3 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x2 = 0 + -3 x2 = 0 + -3 Combine like terms: 0 + -3 = -3 x2 = -3 Simplifying x2 = -3 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

x = {0, -1.414213562, 1.414213562}

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