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Simplifying c2 = 22c + -104 Reorder the terms: c2 = -104 + 22c Solving c2 = -104 + 22c Solving for variable 'c'. Reorder the terms: 104 + -22c + c2 = -104 + 22c + 104 + -22c Reorder the terms: 104 + -22c + c2 = -104 + 104 + 22c + -22c Combine like terms: -104 + 104 = 0 104 + -22c + c2 = 0 + 22c + -22c 104 + -22c + c2 = 22c + -22c Combine like terms: 22c + -22c = 0 104 + -22c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '-104' to each side of the equation. 104 + -22c + -104 + c2 = 0 + -104 Reorder the terms: 104 + -104 + -22c + c2 = 0 + -104 Combine like terms: 104 + -104 = 0 0 + -22c + c2 = 0 + -104 -22c + c2 = 0 + -104 Combine like terms: 0 + -104 = -104 -22c + c2 = -104 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 = -104 + 121 Reorder the terms: 121 + -22c + c2 = -104 + 121 Combine like terms: -104 + 121 = 17 121 + -22c + c2 = 17 Factor a perfect square on the left side: (c + -11)(c + -11) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (c + -11) equal to 4.123105626 and -4.123105626.Subproblem 1
c + -11 = 4.123105626 Simplifying c + -11 = 4.123105626 Reorder the terms: -11 + c = 4.123105626 Solving -11 + c = 4.123105626 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 = 4.123105626 + 11 Combine like terms: -11 + 11 = 0 0 + c = 4.123105626 + 11 c = 4.123105626 + 11 Combine like terms: 4.123105626 + 11 = 15.123105626 c = 15.123105626 Simplifying c = 15.123105626Subproblem 2
c + -11 = -4.123105626 Simplifying c + -11 = -4.123105626 Reorder the terms: -11 + c = -4.123105626 Solving -11 + c = -4.123105626 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 = -4.123105626 + 11 Combine like terms: -11 + 11 = 0 0 + c = -4.123105626 + 11 c = -4.123105626 + 11 Combine like terms: -4.123105626 + 11 = 6.876894374 c = 6.876894374 Simplifying c = 6.876894374Solution
The solution to the problem is based on the solutions from the subproblems. c = {15.123105626, 6.876894374}
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