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Simplifying 24c2 + 44c + 110 = 0 Reorder the terms: 110 + 44c + 24c2 = 0 Solving 110 + 44c + 24c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '2'. 2(55 + 22c + 12c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(55 + 22c + 12c2)' equal to zero and attempt to solve: Simplifying 55 + 22c + 12c2 = 0 Solving 55 + 22c + 12c2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 4.583333333 + 1.833333333c + c2 = 0 Move the constant term to the right: Add '-4.583333333' to each side of the equation. 4.583333333 + 1.833333333c + -4.583333333 + c2 = 0 + -4.583333333 Reorder the terms: 4.583333333 + -4.583333333 + 1.833333333c + c2 = 0 + -4.583333333 Combine like terms: 4.583333333 + -4.583333333 = 0.000000000 0.000000000 + 1.833333333c + c2 = 0 + -4.583333333 1.833333333c + c2 = 0 + -4.583333333 Combine like terms: 0 + -4.583333333 = -4.583333333 1.833333333c + c2 = -4.583333333 The c term is 1.833333333c. Take half its coefficient (0.9166666665). Square it (0.8402777775) and add it to both sides. Add '0.8402777775' to each side of the equation. 1.833333333c + 0.8402777775 + c2 = -4.583333333 + 0.8402777775 Reorder the terms: 0.8402777775 + 1.833333333c + c2 = -4.583333333 + 0.8402777775 Combine like terms: -4.583333333 + 0.8402777775 = -3.7430555555 0.8402777775 + 1.833333333c + c2 = -3.7430555555 Factor a perfect square on the left side: (c + 0.9166666665)(c + 0.9166666665) = -3.7430555555 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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