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Simplifying c2 + 5c = 54 Reorder the terms: 5c + c2 = 54 Solving 5c + c2 = 54 Solving for variable 'c'. Reorder the terms: -54 + 5c + c2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + 5c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + 5c + 54 + c2 = 0 + 54 Reorder the terms: -54 + 54 + 5c + c2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 5c + c2 = 0 + 54 5c + c2 = 0 + 54 Combine like terms: 0 + 54 = 54 5c + c2 = 54 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 = 54 + 6.25 Reorder the terms: 6.25 + 5c + c2 = 54 + 6.25 Combine like terms: 54 + 6.25 = 60.25 6.25 + 5c + c2 = 60.25 Factor a perfect square on the left side: (c + 2.5)(c + 2.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (c + 2.5) equal to 7.762087348 and -7.762087348.Subproblem 1
c + 2.5 = 7.762087348 Simplifying c + 2.5 = 7.762087348 Reorder the terms: 2.5 + c = 7.762087348 Solving 2.5 + c = 7.762087348 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 = 7.762087348 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + c = 7.762087348 + -2.5 c = 7.762087348 + -2.5 Combine like terms: 7.762087348 + -2.5 = 5.262087348 c = 5.262087348 Simplifying c = 5.262087348Subproblem 2
c + 2.5 = -7.762087348 Simplifying c + 2.5 = -7.762087348 Reorder the terms: 2.5 + c = -7.762087348 Solving 2.5 + c = -7.762087348 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 = -7.762087348 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + c = -7.762087348 + -2.5 c = -7.762087348 + -2.5 Combine like terms: -7.762087348 + -2.5 = -10.262087348 c = -10.262087348 Simplifying c = -10.262087348Solution
The solution to the problem is based on the solutions from the subproblems. c = {5.262087348, -10.262087348}
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