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Simplifying x = 36x2 + 12x + 1 Reorder the terms: x = 1 + 12x + 36x2 Solving x = 1 + 12x + 36x2 Solving for variable 'x'. Reorder the terms: -1 + x + -12x + -36x2 = 1 + 12x + 36x2 + -1 + -12x + -36x2 Combine like terms: x + -12x = -11x -1 + -11x + -36x2 = 1 + 12x + 36x2 + -1 + -12x + -36x2 Reorder the terms: -1 + -11x + -36x2 = 1 + -1 + 12x + -12x + 36x2 + -36x2 Combine like terms: 1 + -1 = 0 -1 + -11x + -36x2 = 0 + 12x + -12x + 36x2 + -36x2 -1 + -11x + -36x2 = 12x + -12x + 36x2 + -36x2 Combine like terms: 12x + -12x = 0 -1 + -11x + -36x2 = 0 + 36x2 + -36x2 -1 + -11x + -36x2 = 36x2 + -36x2 Combine like terms: 36x2 + -36x2 = 0 -1 + -11x + -36x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 11x + 36x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 11x + 36x2)' equal to zero and attempt to solve: Simplifying 1 + 11x + 36x2 = 0 Solving 1 + 11x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. 0.02777777778 + 0.3055555556x + x2 = 0 Move the constant term to the right: Add '-0.02777777778' to each side of the equation. 0.02777777778 + 0.3055555556x + -0.02777777778 + x2 = 0 + -0.02777777778 Reorder the terms: 0.02777777778 + -0.02777777778 + 0.3055555556x + x2 = 0 + -0.02777777778 Combine like terms: 0.02777777778 + -0.02777777778 = 0.00000000000 0.00000000000 + 0.3055555556x + x2 = 0 + -0.02777777778 0.3055555556x + x2 = 0 + -0.02777777778 Combine like terms: 0 + -0.02777777778 = -0.02777777778 0.3055555556x + x2 = -0.02777777778 The x term is 0.3055555556x. Take half its coefficient (0.1527777778). Square it (0.02334104939) and add it to both sides. Add '0.02334104939' to each side of the equation. 0.3055555556x + 0.02334104939 + x2 = -0.02777777778 + 0.02334104939 Reorder the terms: 0.02334104939 + 0.3055555556x + x2 = -0.02777777778 + 0.02334104939 Combine like terms: -0.02777777778 + 0.02334104939 = -0.00443672839 0.02334104939 + 0.3055555556x + x2 = -0.00443672839 Factor a perfect square on the left side: (x + 0.1527777778)(x + 0.1527777778) = -0.00443672839 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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