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Simplifying 1.5c2 + 33c + -75 = 52.5 Reorder the terms: -75 + 33c + 1.5c2 = 52.5 Solving -75 + 33c + 1.5c2 = 52.5 Solving for variable 'c'. Reorder the terms: -75 + -52.5 + 33c + 1.5c2 = 52.5 + -52.5 Combine like terms: -75 + -52.5 = -127.5 -127.5 + 33c + 1.5c2 = 52.5 + -52.5 Combine like terms: 52.5 + -52.5 = 0.0 -127.5 + 33c + 1.5c2 = 0.0 Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. -85 + 22c + c2 = 0 Move the constant term to the right: Add '85' to each side of the equation. -85 + 22c + 85 + c2 = 0 + 85 Reorder the terms: -85 + 85 + 22c + c2 = 0 + 85 Combine like terms: -85 + 85 = 0 0 + 22c + c2 = 0 + 85 22c + c2 = 0 + 85 Combine like terms: 0 + 85 = 85 22c + c2 = 85 The c term is 22c. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22c + 121 + c2 = 85 + 121 Reorder the terms: 121 + 22c + c2 = 85 + 121 Combine like terms: 85 + 121 = 206 121 + 22c + c2 = 206 Factor a perfect square on the left side: (c + 11)(c + 11) = 206 Calculate the square root of the right side: 14.352700094 Break this problem into two subproblems by setting (c + 11) equal to 14.352700094 and -14.352700094.Subproblem 1
c + 11 = 14.352700094 Simplifying c + 11 = 14.352700094 Reorder the terms: 11 + c = 14.352700094 Solving 11 + c = 14.352700094 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + c = 14.352700094 + -11 Combine like terms: 11 + -11 = 0 0 + c = 14.352700094 + -11 c = 14.352700094 + -11 Combine like terms: 14.352700094 + -11 = 3.352700094 c = 3.352700094 Simplifying c = 3.352700094Subproblem 2
c + 11 = -14.352700094 Simplifying c + 11 = -14.352700094 Reorder the terms: 11 + c = -14.352700094 Solving 11 + c = -14.352700094 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + c = -14.352700094 + -11 Combine like terms: 11 + -11 = 0 0 + c = -14.352700094 + -11 c = -14.352700094 + -11 Combine like terms: -14.352700094 + -11 = -25.352700094 c = -25.352700094 Simplifying c = -25.352700094Solution
The solution to the problem is based on the solutions from the subproblems. c = {3.352700094, -25.352700094}
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