10x^5-5x^3-30x=0

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Solution for 10x^5-5x^3-30x=0 equation:


Simplifying
10x5 + -5x3 + -30x = 0

Reorder the terms:
-30x + -5x3 + 10x5 = 0

Solving
-30x + -5x3 + 10x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(-6 + -1x2 + 2x4) = 0

Factor a trinomial.
5x((-3 + -2x2)(2 + -1x2)) = 0

Ignore the factor 5.

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 '(-3 + -2x2)' equal to zero and attempt to solve: Simplifying -3 + -2x2 = 0 Solving -3 + -2x2 = 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 + -2x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x2 = 0 + 3 -2x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -2x2 = 3 Divide each side by '-2'. x2 = -1.5 Simplifying x2 = -1.5 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 '(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}

Solution

x = {0, -1.414213562, 1.414213562}

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