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Simplifying c2 + 108c + 108 = 0 Reorder the terms: 108 + 108c + c2 = 0 Solving 108 + 108c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '-108' to each side of the equation. 108 + 108c + -108 + c2 = 0 + -108 Reorder the terms: 108 + -108 + 108c + c2 = 0 + -108 Combine like terms: 108 + -108 = 0 0 + 108c + c2 = 0 + -108 108c + c2 = 0 + -108 Combine like terms: 0 + -108 = -108 108c + c2 = -108 The c term is 108c. Take half its coefficient (54). Square it (2916) and add it to both sides. Add '2916' to each side of the equation. 108c + 2916 + c2 = -108 + 2916 Reorder the terms: 2916 + 108c + c2 = -108 + 2916 Combine like terms: -108 + 2916 = 2808 2916 + 108c + c2 = 2808 Factor a perfect square on the left side: (c + 54)(c + 54) = 2808 Calculate the square root of the right side: 52.990565198 Break this problem into two subproblems by setting (c + 54) equal to 52.990565198 and -52.990565198.Subproblem 1
c + 54 = 52.990565198 Simplifying c + 54 = 52.990565198 Reorder the terms: 54 + c = 52.990565198 Solving 54 + c = 52.990565198 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-54' to each side of the equation. 54 + -54 + c = 52.990565198 + -54 Combine like terms: 54 + -54 = 0 0 + c = 52.990565198 + -54 c = 52.990565198 + -54 Combine like terms: 52.990565198 + -54 = -1.009434802 c = -1.009434802 Simplifying c = -1.009434802Subproblem 2
c + 54 = -52.990565198 Simplifying c + 54 = -52.990565198 Reorder the terms: 54 + c = -52.990565198 Solving 54 + c = -52.990565198 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-54' to each side of the equation. 54 + -54 + c = -52.990565198 + -54 Combine like terms: 54 + -54 = 0 0 + c = -52.990565198 + -54 c = -52.990565198 + -54 Combine like terms: -52.990565198 + -54 = -106.990565198 c = -106.990565198 Simplifying c = -106.990565198Solution
The solution to the problem is based on the solutions from the subproblems. c = {-1.009434802, -106.990565198}
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