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Simplifying 4c2 + 44c + 85 = 3 Reorder the terms: 85 + 44c + 4c2 = 3 Solving 85 + 44c + 4c2 = 3 Solving for variable 'c'. Reorder the terms: 85 + -3 + 44c + 4c2 = 3 + -3 Combine like terms: 85 + -3 = 82 82 + 44c + 4c2 = 3 + -3 Combine like terms: 3 + -3 = 0 82 + 44c + 4c2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(41 + 22c + 2c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(41 + 22c + 2c2)' equal to zero and attempt to solve: Simplifying 41 + 22c + 2c2 = 0 Solving 41 + 22c + 2c2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 20.5 + 11c + c2 = 0 Move the constant term to the right: Add '-20.5' to each side of the equation. 20.5 + 11c + -20.5 + c2 = 0 + -20.5 Reorder the terms: 20.5 + -20.5 + 11c + c2 = 0 + -20.5 Combine like terms: 20.5 + -20.5 = 0.0 0.0 + 11c + c2 = 0 + -20.5 11c + c2 = 0 + -20.5 Combine like terms: 0 + -20.5 = -20.5 11c + c2 = -20.5 The c term is 11c. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11c + 30.25 + c2 = -20.5 + 30.25 Reorder the terms: 30.25 + 11c + c2 = -20.5 + 30.25 Combine like terms: -20.5 + 30.25 = 9.75 30.25 + 11c + c2 = 9.75 Factor a perfect square on the left side: (c + 5.5)(c + 5.5) = 9.75 Calculate the square root of the right side: 3.122498999 Break this problem into two subproblems by setting (c + 5.5) equal to 3.122498999 and -3.122498999.Subproblem 1
c + 5.5 = 3.122498999 Simplifying c + 5.5 = 3.122498999 Reorder the terms: 5.5 + c = 3.122498999 Solving 5.5 + c = 3.122498999 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + c = 3.122498999 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + c = 3.122498999 + -5.5 c = 3.122498999 + -5.5 Combine like terms: 3.122498999 + -5.5 = -2.377501001 c = -2.377501001 Simplifying c = -2.377501001Subproblem 2
c + 5.5 = -3.122498999 Simplifying c + 5.5 = -3.122498999 Reorder the terms: 5.5 + c = -3.122498999 Solving 5.5 + c = -3.122498999 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + c = -3.122498999 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + c = -3.122498999 + -5.5 c = -3.122498999 + -5.5 Combine like terms: -3.122498999 + -5.5 = -8.622498999 c = -8.622498999 Simplifying c = -8.622498999Solution
The solution to the problem is based on the solutions from the subproblems. c = {-2.377501001, -8.622498999}Solution
c = {-2.377501001, -8.622498999}
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