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Simplifying (6c2 + -1c + -1) + -1(4 + -2c2 + -8c) = 0 Reorder the terms: (-1 + -1c + 6c2) + -1(4 + -2c2 + -8c) = 0 Remove parenthesis around (-1 + -1c + 6c2) -1 + -1c + 6c2 + -1(4 + -2c2 + -8c) = 0 Reorder the terms: -1 + -1c + 6c2 + -1(4 + -8c + -2c2) = 0 -1 + -1c + 6c2 + (4 * -1 + -8c * -1 + -2c2 * -1) = 0 -1 + -1c + 6c2 + (-4 + 8c + 2c2) = 0 Reorder the terms: -1 + -4 + -1c + 8c + 6c2 + 2c2 = 0 Combine like terms: -1 + -4 = -5 -5 + -1c + 8c + 6c2 + 2c2 = 0 Combine like terms: -1c + 8c = 7c -5 + 7c + 6c2 + 2c2 = 0 Combine like terms: 6c2 + 2c2 = 8c2 -5 + 7c + 8c2 = 0 Solving -5 + 7c + 8c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + 0.875c + c2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 0.875c + 0.625 + c2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 0.875c + c2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 0.875c + c2 = 0 + 0.625 0.875c + c2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 0.875c + c2 = 0.625 The c term is 0.875c. Take half its coefficient (0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. 0.875c + 0.19140625 + c2 = 0.625 + 0.19140625 Reorder the terms: 0.19140625 + 0.875c + c2 = 0.625 + 0.19140625 Combine like terms: 0.625 + 0.19140625 = 0.81640625 0.19140625 + 0.875c + c2 = 0.81640625 Factor a perfect square on the left side: (c + 0.4375)(c + 0.4375) = 0.81640625 Calculate the square root of the right side: 0.903552018 Break this problem into two subproblems by setting (c + 0.4375) equal to 0.903552018 and -0.903552018.Subproblem 1
c + 0.4375 = 0.903552018 Simplifying c + 0.4375 = 0.903552018 Reorder the terms: 0.4375 + c = 0.903552018 Solving 0.4375 + c = 0.903552018 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + c = 0.903552018 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + c = 0.903552018 + -0.4375 c = 0.903552018 + -0.4375 Combine like terms: 0.903552018 + -0.4375 = 0.466052018 c = 0.466052018 Simplifying c = 0.466052018Subproblem 2
c + 0.4375 = -0.903552018 Simplifying c + 0.4375 = -0.903552018 Reorder the terms: 0.4375 + c = -0.903552018 Solving 0.4375 + c = -0.903552018 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + c = -0.903552018 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + c = -0.903552018 + -0.4375 c = -0.903552018 + -0.4375 Combine like terms: -0.903552018 + -0.4375 = -1.341052018 c = -1.341052018 Simplifying c = -1.341052018Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.466052018, -1.341052018}
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