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Simplifying C = 3(2 + -1C) + 7C(C + 2) C = (2 * 3 + -1C * 3) + 7C(C + 2) C = (6 + -3C) + 7C(C + 2) Reorder the terms: C = 6 + -3C + 7C(2 + C) C = 6 + -3C + (2 * 7C + C * 7C) C = 6 + -3C + (14C + 7C2) Combine like terms: -3C + 14C = 11C C = 6 + 11C + 7C2 Solving C = 6 + 11C + 7C2 Solving for variable 'C'. Reorder the terms: -6 + C + -11C + -7C2 = 6 + 11C + 7C2 + -6 + -11C + -7C2 Combine like terms: C + -11C = -10C -6 + -10C + -7C2 = 6 + 11C + 7C2 + -6 + -11C + -7C2 Reorder the terms: -6 + -10C + -7C2 = 6 + -6 + 11C + -11C + 7C2 + -7C2 Combine like terms: 6 + -6 = 0 -6 + -10C + -7C2 = 0 + 11C + -11C + 7C2 + -7C2 -6 + -10C + -7C2 = 11C + -11C + 7C2 + -7C2 Combine like terms: 11C + -11C = 0 -6 + -10C + -7C2 = 0 + 7C2 + -7C2 -6 + -10C + -7C2 = 7C2 + -7C2 Combine like terms: 7C2 + -7C2 = 0 -6 + -10C + -7C2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 10C + 7C2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + 10C + 7C2)' equal to zero and attempt to solve: Simplifying 6 + 10C + 7C2 = 0 Solving 6 + 10C + 7C2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.8571428571 + 1.428571429C + C2 = 0 Move the constant term to the right: Add '-0.8571428571' to each side of the equation. 0.8571428571 + 1.428571429C + -0.8571428571 + C2 = 0 + -0.8571428571 Reorder the terms: 0.8571428571 + -0.8571428571 + 1.428571429C + C2 = 0 + -0.8571428571 Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000 0.0000000000 + 1.428571429C + C2 = 0 + -0.8571428571 1.428571429C + C2 = 0 + -0.8571428571 Combine like terms: 0 + -0.8571428571 = -0.8571428571 1.428571429C + C2 = -0.8571428571 The C term is 1.428571429C. Take half its coefficient (0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. 1.428571429C + 0.5102040819 + C2 = -0.8571428571 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429C + C2 = -0.8571428571 + 0.5102040819 Combine like terms: -0.8571428571 + 0.5102040819 = -0.3469387752 0.5102040819 + 1.428571429C + C2 = -0.3469387752 Factor a perfect square on the left side: (C + 0.7142857145)(C + 0.7142857145) = -0.3469387752 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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