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Simplifying 0 = x5 + x3 + 12x Reorder the terms: 0 = 12x + x3 + x5 Solving 0 = 12x + x3 + x5 Solving for variable 'x'. Remove the zero: -12x + -1x3 + -1x5 = 12x + x3 + x5 + -12x + -1x3 + -1x5 Reorder the terms: -12x + -1x3 + -1x5 = 12x + -12x + x3 + -1x3 + x5 + -1x5 Combine like terms: 12x + -12x = 0 -12x + -1x3 + -1x5 = 0 + x3 + -1x3 + x5 + -1x5 -12x + -1x3 + -1x5 = x3 + -1x3 + x5 + -1x5 Combine like terms: x3 + -1x3 = 0 -12x + -1x3 + -1x5 = 0 + x5 + -1x5 -12x + -1x3 + -1x5 = x5 + -1x5 Combine like terms: x5 + -1x5 = 0 -12x + -1x3 + -1x5 = 0 Factor out the Greatest Common Factor (GCF), '-1x'. -1x(12 + x2 + x4) = 0 Ignore the factor -1.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 = 0Subproblem 2
Set the factor '(12 + x2 + x4)' equal to zero and attempt to solve: Simplifying 12 + x2 + x4 = 0 Solving 12 + x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + x2 + -12 + x4 = 0 + -12 Reorder the terms: 12 + -12 + x2 + x4 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + x2 + x4 = 0 + -12 x2 + x4 = 0 + -12 Combine like terms: 0 + -12 = -12 x2 + x4 = -12 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. x2 + 0.25 + x4 = -12 + 0.25 Reorder the terms: 0.25 + x2 + x4 = -12 + 0.25 Combine like terms: -12 + 0.25 = -11.75 0.25 + x2 + x4 = -11.75 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = -11.75 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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