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Simplifying 12x5 + 6x3 + 27x = 0 Reorder the terms: 27x + 6x3 + 12x5 = 0 Solving 27x + 6x3 + 12x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(9 + 2x2 + 4x4) = 0 Ignore the factor 3.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 '(9 + 2x2 + 4x4)' equal to zero and attempt to solve: Simplifying 9 + 2x2 + 4x4 = 0 Solving 9 + 2x2 + 4x4 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + 0.5x2 + x4 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 0.5x2 + -2.25 + x4 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 0.5x2 + x4 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 0.5x2 + x4 = 0 + -2.25 0.5x2 + x4 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 0.5x2 + x4 = -2.25 The x term is 0.5x2. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x2 + 0.0625 + x4 = -2.25 + 0.0625 Reorder the terms: 0.0625 + 0.5x2 + x4 = -2.25 + 0.0625 Combine like terms: -2.25 + 0.0625 = -2.1875 0.0625 + 0.5x2 + x4 = -2.1875 Factor a perfect square on the left side: (x2 + 0.25)(x2 + 0.25) = -2.1875 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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