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Simplifying 2c(4c + -1) + -6 = 5c + 4 Reorder the terms: 2c(-1 + 4c) + -6 = 5c + 4 (-1 * 2c + 4c * 2c) + -6 = 5c + 4 (-2c + 8c2) + -6 = 5c + 4 Reorder the terms: -6 + -2c + 8c2 = 5c + 4 Reorder the terms: -6 + -2c + 8c2 = 4 + 5c Solving -6 + -2c + 8c2 = 4 + 5c Solving for variable 'c'. Reorder the terms: -6 + -4 + -2c + -5c + 8c2 = 4 + 5c + -4 + -5c Combine like terms: -6 + -4 = -10 -10 + -2c + -5c + 8c2 = 4 + 5c + -4 + -5c Combine like terms: -2c + -5c = -7c -10 + -7c + 8c2 = 4 + 5c + -4 + -5c Reorder the terms: -10 + -7c + 8c2 = 4 + -4 + 5c + -5c Combine like terms: 4 + -4 = 0 -10 + -7c + 8c2 = 0 + 5c + -5c -10 + -7c + 8c2 = 5c + -5c Combine like terms: 5c + -5c = 0 -10 + -7c + 8c2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.25 + -0.875c + c2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -0.875c + 1.25 + c2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -0.875c + c2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -0.875c + c2 = 0 + 1.25 -0.875c + c2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -0.875c + c2 = 1.25 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 = 1.25 + 0.19140625 Reorder the terms: 0.19140625 + -0.875c + c2 = 1.25 + 0.19140625 Combine like terms: 1.25 + 0.19140625 = 1.44140625 0.19140625 + -0.875c + c2 = 1.44140625 Factor a perfect square on the left side: (c + -0.4375)(c + -0.4375) = 1.44140625 Calculate the square root of the right side: 1.200585795 Break this problem into two subproblems by setting (c + -0.4375) equal to 1.200585795 and -1.200585795.Subproblem 1
c + -0.4375 = 1.200585795 Simplifying c + -0.4375 = 1.200585795 Reorder the terms: -0.4375 + c = 1.200585795 Solving -0.4375 + c = 1.200585795 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 = 1.200585795 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + c = 1.200585795 + 0.4375 c = 1.200585795 + 0.4375 Combine like terms: 1.200585795 + 0.4375 = 1.638085795 c = 1.638085795 Simplifying c = 1.638085795Subproblem 2
c + -0.4375 = -1.200585795 Simplifying c + -0.4375 = -1.200585795 Reorder the terms: -0.4375 + c = -1.200585795 Solving -0.4375 + c = -1.200585795 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 = -1.200585795 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + c = -1.200585795 + 0.4375 c = -1.200585795 + 0.4375 Combine like terms: -1.200585795 + 0.4375 = -0.763085795 c = -0.763085795 Simplifying c = -0.763085795Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.638085795, -0.763085795}
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