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Simplifying x5 + 20x3 + 120x = 0 Reorder the terms: 120x + 20x3 + x5 = 0 Solving 120x + 20x3 + x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(120 + 20x2 + 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 '(120 + 20x2 + x4)' equal to zero and attempt to solve: Simplifying 120 + 20x2 + x4 = 0 Solving 120 + 20x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-120' to each side of the equation. 120 + 20x2 + -120 + x4 = 0 + -120 Reorder the terms: 120 + -120 + 20x2 + x4 = 0 + -120 Combine like terms: 120 + -120 = 0 0 + 20x2 + x4 = 0 + -120 20x2 + x4 = 0 + -120 Combine like terms: 0 + -120 = -120 20x2 + x4 = -120 The x term is 20x2. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x2 + 100 + x4 = -120 + 100 Reorder the terms: 100 + 20x2 + x4 = -120 + 100 Combine like terms: -120 + 100 = -20 100 + 20x2 + x4 = -20 Factor a perfect square on the left side: (x2 + 10)(x2 + 10) = -20 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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