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Simplifying x5 + -5x3 + 12x = 0 Reorder the terms: 12x + -5x3 + x5 = 0 Solving 12x + -5x3 + x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(12 + -5x2 + 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 '(12 + -5x2 + x4)' equal to zero and attempt to solve: Simplifying 12 + -5x2 + x4 = 0 Solving 12 + -5x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -5x2 + -12 + x4 = 0 + -12 Reorder the terms: 12 + -12 + -5x2 + x4 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -5x2 + x4 = 0 + -12 -5x2 + x4 = 0 + -12 Combine like terms: 0 + -12 = -12 -5x2 + x4 = -12 The x term is -5x2. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x2 + 6.25 + x4 = -12 + 6.25 Reorder the terms: 6.25 + -5x2 + x4 = -12 + 6.25 Combine like terms: -12 + 6.25 = -5.75 6.25 + -5x2 + x4 = -5.75 Factor a perfect square on the left side: (x2 + -2.5)(x2 + -2.5) = -5.75 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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