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Simplifying 8c2 + 34c + 11 = 0 Reorder the terms: 11 + 34c + 8c2 = 0 Solving 11 + 34c + 8c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.375 + 4.25c + c2 = 0 Move the constant term to the right: Add '-1.375' to each side of the equation. 1.375 + 4.25c + -1.375 + c2 = 0 + -1.375 Reorder the terms: 1.375 + -1.375 + 4.25c + c2 = 0 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + 4.25c + c2 = 0 + -1.375 4.25c + c2 = 0 + -1.375 Combine like terms: 0 + -1.375 = -1.375 4.25c + c2 = -1.375 The c term is 4.25c. Take half its coefficient (2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. 4.25c + 4.515625 + c2 = -1.375 + 4.515625 Reorder the terms: 4.515625 + 4.25c + c2 = -1.375 + 4.515625 Combine like terms: -1.375 + 4.515625 = 3.140625 4.515625 + 4.25c + c2 = 3.140625 Factor a perfect square on the left side: (c + 2.125)(c + 2.125) = 3.140625 Calculate the square root of the right side: 1.77218086 Break this problem into two subproblems by setting (c + 2.125) equal to 1.77218086 and -1.77218086.Subproblem 1
c + 2.125 = 1.77218086 Simplifying c + 2.125 = 1.77218086 Reorder the terms: 2.125 + c = 1.77218086 Solving 2.125 + c = 1.77218086 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + c = 1.77218086 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + c = 1.77218086 + -2.125 c = 1.77218086 + -2.125 Combine like terms: 1.77218086 + -2.125 = -0.35281914 c = -0.35281914 Simplifying c = -0.35281914Subproblem 2
c + 2.125 = -1.77218086 Simplifying c + 2.125 = -1.77218086 Reorder the terms: 2.125 + c = -1.77218086 Solving 2.125 + c = -1.77218086 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + c = -1.77218086 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + c = -1.77218086 + -2.125 c = -1.77218086 + -2.125 Combine like terms: -1.77218086 + -2.125 = -3.89718086 c = -3.89718086 Simplifying c = -3.89718086Solution
The solution to the problem is based on the solutions from the subproblems. c = {-0.35281914, -3.89718086}
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