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Simplifying 6c2 + -27 = 11c Reorder the terms: -27 + 6c2 = 11c Solving -27 + 6c2 = 11c Solving for variable 'c'. Reorder the terms: -27 + -11c + 6c2 = 11c + -11c Combine like terms: 11c + -11c = 0 -27 + -11c + 6c2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -4.5 + -1.833333333c + c2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -1.833333333c + 4.5 + c2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -1.833333333c + c2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -1.833333333c + c2 = 0 + 4.5 -1.833333333c + c2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -1.833333333c + c2 = 4.5 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 = 4.5 + 0.8402777775 Reorder the terms: 0.8402777775 + -1.833333333c + c2 = 4.5 + 0.8402777775 Combine like terms: 4.5 + 0.8402777775 = 5.3402777775 0.8402777775 + -1.833333333c + c2 = 5.3402777775 Factor a perfect square on the left side: (c + -0.9166666665)(c + -0.9166666665) = 5.3402777775 Calculate the square root of the right side: 2.310904104 Break this problem into two subproblems by setting (c + -0.9166666665) equal to 2.310904104 and -2.310904104.Subproblem 1
c + -0.9166666665 = 2.310904104 Simplifying c + -0.9166666665 = 2.310904104 Reorder the terms: -0.9166666665 + c = 2.310904104 Solving -0.9166666665 + c = 2.310904104 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + c = 2.310904104 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + c = 2.310904104 + 0.9166666665 c = 2.310904104 + 0.9166666665 Combine like terms: 2.310904104 + 0.9166666665 = 3.2275707705 c = 3.2275707705 Simplifying c = 3.2275707705Subproblem 2
c + -0.9166666665 = -2.310904104 Simplifying c + -0.9166666665 = -2.310904104 Reorder the terms: -0.9166666665 + c = -2.310904104 Solving -0.9166666665 + c = -2.310904104 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + c = -2.310904104 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + c = -2.310904104 + 0.9166666665 c = -2.310904104 + 0.9166666665 Combine like terms: -2.310904104 + 0.9166666665 = -1.3942374375 c = -1.3942374375 Simplifying c = -1.3942374375Solution
The solution to the problem is based on the solutions from the subproblems. c = {3.2275707705, -1.3942374375}
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