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Simplifying 12x5 + -6x3 + 7x + -3x5 + 5x3 + x = 0 Reorder the terms: 7x + x + -6x3 + 5x3 + 12x5 + -3x5 = 0 Combine like terms: 7x + x = 8x 8x + -6x3 + 5x3 + 12x5 + -3x5 = 0 Combine like terms: -6x3 + 5x3 = -1x3 8x + -1x3 + 12x5 + -3x5 = 0 Combine like terms: 12x5 + -3x5 = 9x5 8x + -1x3 + 9x5 = 0 Solving 8x + -1x3 + 9x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(8 + -1x2 + 9x4) = 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 '(8 + -1x2 + 9x4)' equal to zero and attempt to solve: Simplifying 8 + -1x2 + 9x4 = 0 Solving 8 + -1x2 + 9x4 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.8888888889 + -0.1111111111x2 + x4 = 0 Move the constant term to the right: Add '-0.8888888889' to each side of the equation. 0.8888888889 + -0.1111111111x2 + -0.8888888889 + x4 = 0 + -0.8888888889 Reorder the terms: 0.8888888889 + -0.8888888889 + -0.1111111111x2 + x4 = 0 + -0.8888888889 Combine like terms: 0.8888888889 + -0.8888888889 = 0.0000000000 0.0000000000 + -0.1111111111x2 + x4 = 0 + -0.8888888889 -0.1111111111x2 + x4 = 0 + -0.8888888889 Combine like terms: 0 + -0.8888888889 = -0.8888888889 -0.1111111111x2 + x4 = -0.8888888889 The x term is -0.1111111111x2. Take half its coefficient (-0.05555555555). Square it (0.003086419752) and add it to both sides. Add '0.003086419752' to each side of the equation. -0.1111111111x2 + 0.003086419752 + x4 = -0.8888888889 + 0.003086419752 Reorder the terms: 0.003086419752 + -0.1111111111x2 + x4 = -0.8888888889 + 0.003086419752 Combine like terms: -0.8888888889 + 0.003086419752 = -0.885802469148 0.003086419752 + -0.1111111111x2 + x4 = -0.885802469148 Factor a perfect square on the left side: (x2 + -0.05555555555)(x2 + -0.05555555555) = -0.885802469148 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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