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Simplifying 0 = 14C2 + 14C + 15 Reorder the terms: 0 = 15 + 14C + 14C2 Solving 0 = 15 + 14C + 14C2 Solving for variable 'C'. Combine like terms: 0 + -15 = -15 -15 + -14C + -14C2 = 15 + 14C + 14C2 + -15 + -14C + -14C2 Reorder the terms: -15 + -14C + -14C2 = 15 + -15 + 14C + -14C + 14C2 + -14C2 Combine like terms: 15 + -15 = 0 -15 + -14C + -14C2 = 0 + 14C + -14C + 14C2 + -14C2 -15 + -14C + -14C2 = 14C + -14C + 14C2 + -14C2 Combine like terms: 14C + -14C = 0 -15 + -14C + -14C2 = 0 + 14C2 + -14C2 -15 + -14C + -14C2 = 14C2 + -14C2 Combine like terms: 14C2 + -14C2 = 0 -15 + -14C + -14C2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 14C + 14C2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(15 + 14C + 14C2)' equal to zero and attempt to solve: Simplifying 15 + 14C + 14C2 = 0 Solving 15 + 14C + 14C2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 1.071428571 + C + C2 = 0 Move the constant term to the right: Add '-1.071428571' to each side of the equation. 1.071428571 + C + -1.071428571 + C2 = 0 + -1.071428571 Reorder the terms: 1.071428571 + -1.071428571 + C + C2 = 0 + -1.071428571 Combine like terms: 1.071428571 + -1.071428571 = 0.000000000 0.000000000 + C + C2 = 0 + -1.071428571 C + C2 = 0 + -1.071428571 Combine like terms: 0 + -1.071428571 = -1.071428571 C + C2 = -1.071428571 The C term is C. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + C2 = -1.071428571 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + C2 = -1.071428571 + 0.25 Combine like terms: -1.071428571 + 0.25 = -0.821428571 1.25 + C2 = -0.821428571 Factor a perfect square on the left side: (C + 0.5)(C + 0.5) = -0.821428571 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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