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Simplifying x5 + 3x3 + 6x = 0 Reorder the terms: 6x + 3x3 + x5 = 0 Solving 6x + 3x3 + x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(6 + 3x2 + x4) = 0Subproblem 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 = 0Subproblem 2
Set the factor '(6 + 3x2 + x4)' equal to zero and attempt to solve: Simplifying 6 + 3x2 + x4 = 0 Solving 6 + 3x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 3x2 + -6 + x4 = 0 + -6 Reorder the terms: 6 + -6 + 3x2 + x4 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 3x2 + x4 = 0 + -6 3x2 + x4 = 0 + -6 Combine like terms: 0 + -6 = -6 3x2 + x4 = -6 The x term is 3x2. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x2 + 2.25 + x4 = -6 + 2.25 Reorder the terms: 2.25 + 3x2 + x4 = -6 + 2.25 Combine like terms: -6 + 2.25 = -3.75 2.25 + 3x2 + x4 = -3.75 Factor a perfect square on the left side: (x2 + 1.5)(x2 + 1.5) = -3.75 Can't calculate square root of the right side. 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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