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

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


Simplifying
5x5 + 5x3 + -6x = 0

Reorder the terms:
-6x + 5x3 + 5x5 = 0

Solving
-6x + 5x3 + 5x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-6 + 5x2 + 5x4) = 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 '(-6 + 5x2 + 5x4)' equal to zero and attempt to solve: Simplifying -6 + 5x2 + 5x4 = 0 Solving -6 + 5x2 + 5x4 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + x2 + x4 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + x2 + 1.2 + x4 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + x2 + x4 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x2 + x4 = 0 + 1.2 x2 + x4 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 x2 + x4 = 1.2 The x term is x2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x4 = 1.2 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x4 = 1.2 + 0.25 Combine like terms: 1.2 + 0.25 = 1.45 1.25 + x4 = 1.45 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 1.45 Calculate the square root of the right side: 1.204159458 Break this problem into two subproblems by setting (x2 + 0.5) equal to 1.204159458 and -1.204159458.

Subproblem 1

x2 + 0.5 = 1.204159458 Simplifying x2 + 0.5 = 1.204159458 Reorder the terms: 0.5 + x2 = 1.204159458 Solving 0.5 + x2 = 1.204159458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = 1.204159458 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 1.204159458 + -0.5 x2 = 1.204159458 + -0.5 Combine like terms: 1.204159458 + -0.5 = 0.704159458 x2 = 0.704159458 Simplifying x2 = 0.704159458 Take the square root of each side: x = {-0.839142096, 0.839142096}

Subproblem 2

x2 + 0.5 = -1.204159458 Simplifying x2 + 0.5 = -1.204159458 Reorder the terms: 0.5 + x2 = -1.204159458 Solving 0.5 + x2 = -1.204159458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = -1.204159458 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -1.204159458 + -0.5 x2 = -1.204159458 + -0.5 Combine like terms: -1.204159458 + -0.5 = -1.704159458 x2 = -1.704159458 Simplifying x2 = -1.704159458 Reorder the terms: 1.704159458 + x2 = -1.704159458 + 1.704159458 Combine like terms: -1.704159458 + 1.704159458 = 0.000000000 1.704159458 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. 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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