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Simplifying C2 + 5C = 100 Reorder the terms: 5C + C2 = 100 Solving 5C + C2 = 100 Solving for variable 'C'. Reorder the terms: -100 + 5C + C2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 5C + C2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 5C + 100 + C2 = 0 + 100 Reorder the terms: -100 + 100 + 5C + C2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 5C + C2 = 0 + 100 5C + C2 = 0 + 100 Combine like terms: 0 + 100 = 100 5C + C2 = 100 The C term is 5C. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5C + 6.25 + C2 = 100 + 6.25 Reorder the terms: 6.25 + 5C + C2 = 100 + 6.25 Combine like terms: 100 + 6.25 = 106.25 6.25 + 5C + C2 = 106.25 Factor a perfect square on the left side: (C + 2.5)(C + 2.5) = 106.25 Calculate the square root of the right side: 10.307764064 Break this problem into two subproblems by setting (C + 2.5) equal to 10.307764064 and -10.307764064.Subproblem 1
C + 2.5 = 10.307764064 Simplifying C + 2.5 = 10.307764064 Reorder the terms: 2.5 + C = 10.307764064 Solving 2.5 + C = 10.307764064 Solving for variable 'C'. Move all terms containing C to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + C = 10.307764064 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + C = 10.307764064 + -2.5 C = 10.307764064 + -2.5 Combine like terms: 10.307764064 + -2.5 = 7.807764064 C = 7.807764064 Simplifying C = 7.807764064Subproblem 2
C + 2.5 = -10.307764064 Simplifying C + 2.5 = -10.307764064 Reorder the terms: 2.5 + C = -10.307764064 Solving 2.5 + C = -10.307764064 Solving for variable 'C'. Move all terms containing C to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + C = -10.307764064 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + C = -10.307764064 + -2.5 C = -10.307764064 + -2.5 Combine like terms: -10.307764064 + -2.5 = -12.807764064 C = -12.807764064 Simplifying C = -12.807764064Solution
The solution to the problem is based on the solutions from the subproblems. C = {7.807764064, -12.807764064}
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