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Simplifying 36x4 + 12x2 + 2 = 0 Reorder the terms: 2 + 12x2 + 36x4 = 0 Solving 2 + 12x2 + 36x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 6x2 + 18x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 6x2 + 18x4)' equal to zero and attempt to solve: Simplifying 1 + 6x2 + 18x4 = 0 Solving 1 + 6x2 + 18x4 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.05555555556 + 0.3333333333x2 + x4 = 0 Move the constant term to the right: Add '-0.05555555556' to each side of the equation. 0.05555555556 + 0.3333333333x2 + -0.05555555556 + x4 = 0 + -0.05555555556 Reorder the terms: 0.05555555556 + -0.05555555556 + 0.3333333333x2 + x4 = 0 + -0.05555555556 Combine like terms: 0.05555555556 + -0.05555555556 = 0.00000000000 0.00000000000 + 0.3333333333x2 + x4 = 0 + -0.05555555556 0.3333333333x2 + x4 = 0 + -0.05555555556 Combine like terms: 0 + -0.05555555556 = -0.05555555556 0.3333333333x2 + x4 = -0.05555555556 The x term is 0.3333333333x2. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x2 + 0.02777777779 + x4 = -0.05555555556 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x2 + x4 = -0.05555555556 + 0.02777777779 Combine like terms: -0.05555555556 + 0.02777777779 = -0.02777777777 0.02777777779 + 0.3333333333x2 + x4 = -0.02777777777 Factor a perfect square on the left side: (x2 + 0.1666666667)(x2 + 0.1666666667) = -0.02777777777 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. The solution to this equation could not be determined.
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