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Simplifying 36 + -1(3c + 4) = 2(c + 4) * c Reorder the terms: 36 + -1(4 + 3c) = 2(c + 4) * c 36 + (4 * -1 + 3c * -1) = 2(c + 4) * c 36 + (-4 + -3c) = 2(c + 4) * c Combine like terms: 36 + -4 = 32 32 + -3c = 2(c + 4) * c Reorder the terms: 32 + -3c = 2(4 + c) * c Reorder the terms for easier multiplication: 32 + -3c = 2c(4 + c) 32 + -3c = (4 * 2c + c * 2c) 32 + -3c = (8c + 2c2) Solving 32 + -3c = 8c + 2c2 Solving for variable 'c'. Combine like terms: -3c + -8c = -11c 32 + -11c + -2c2 = 8c + 2c2 + -8c + -2c2 Reorder the terms: 32 + -11c + -2c2 = 8c + -8c + 2c2 + -2c2 Combine like terms: 8c + -8c = 0 32 + -11c + -2c2 = 0 + 2c2 + -2c2 32 + -11c + -2c2 = 2c2 + -2c2 Combine like terms: 2c2 + -2c2 = 0 32 + -11c + -2c2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -16 + 5.5c + c2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 5.5c + 16 + c2 = 0 + 16 Reorder the terms: -16 + 16 + 5.5c + c2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 5.5c + c2 = 0 + 16 5.5c + c2 = 0 + 16 Combine like terms: 0 + 16 = 16 5.5c + c2 = 16 The c term is 5.5c. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5c + 7.5625 + c2 = 16 + 7.5625 Reorder the terms: 7.5625 + 5.5c + c2 = 16 + 7.5625 Combine like terms: 16 + 7.5625 = 23.5625 7.5625 + 5.5c + c2 = 23.5625 Factor a perfect square on the left side: (c + 2.75)(c + 2.75) = 23.5625 Calculate the square root of the right side: 4.85412196 Break this problem into two subproblems by setting (c + 2.75) equal to 4.85412196 and -4.85412196.Subproblem 1
c + 2.75 = 4.85412196 Simplifying c + 2.75 = 4.85412196 Reorder the terms: 2.75 + c = 4.85412196 Solving 2.75 + c = 4.85412196 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + c = 4.85412196 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + c = 4.85412196 + -2.75 c = 4.85412196 + -2.75 Combine like terms: 4.85412196 + -2.75 = 2.10412196 c = 2.10412196 Simplifying c = 2.10412196Subproblem 2
c + 2.75 = -4.85412196 Simplifying c + 2.75 = -4.85412196 Reorder the terms: 2.75 + c = -4.85412196 Solving 2.75 + c = -4.85412196 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + c = -4.85412196 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + c = -4.85412196 + -2.75 c = -4.85412196 + -2.75 Combine like terms: -4.85412196 + -2.75 = -7.60412196 c = -7.60412196 Simplifying c = -7.60412196Solution
The solution to the problem is based on the solutions from the subproblems. c = {2.10412196, -7.60412196}
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