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Simplifying -4c2 + -12c + 5 = 0 Reorder the terms: 5 + -12c + -4c2 = 0 Solving 5 + -12c + -4c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.25 + 3c + c2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 3c + 1.25 + c2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 3c + c2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 3c + c2 = 0 + 1.25 3c + c2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 3c + c2 = 1.25 The c term is 3c. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3c + 2.25 + c2 = 1.25 + 2.25 Reorder the terms: 2.25 + 3c + c2 = 1.25 + 2.25 Combine like terms: 1.25 + 2.25 = 3.5 2.25 + 3c + c2 = 3.5 Factor a perfect square on the left side: (c + 1.5)(c + 1.5) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting (c + 1.5) equal to 1.870828693 and -1.870828693.Subproblem 1
c + 1.5 = 1.870828693 Simplifying c + 1.5 = 1.870828693 Reorder the terms: 1.5 + c = 1.870828693 Solving 1.5 + c = 1.870828693 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + c = 1.870828693 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + c = 1.870828693 + -1.5 c = 1.870828693 + -1.5 Combine like terms: 1.870828693 + -1.5 = 0.370828693 c = 0.370828693 Simplifying c = 0.370828693Subproblem 2
c + 1.5 = -1.870828693 Simplifying c + 1.5 = -1.870828693 Reorder the terms: 1.5 + c = -1.870828693 Solving 1.5 + c = -1.870828693 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + c = -1.870828693 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + c = -1.870828693 + -1.5 c = -1.870828693 + -1.5 Combine like terms: -1.870828693 + -1.5 = -3.370828693 c = -3.370828693 Simplifying c = -3.370828693Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.370828693, -3.370828693}
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