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Simplifying 27c2 + 108c + -3510 = 0 Reorder the terms: -3510 + 108c + 27c2 = 0 Solving -3510 + 108c + 27c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '27'. 27(-130 + 4c + c2) = 0 Ignore the factor 27.Subproblem 1
Set the factor '(-130 + 4c + c2)' equal to zero and attempt to solve: Simplifying -130 + 4c + c2 = 0 Solving -130 + 4c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '130' to each side of the equation. -130 + 4c + 130 + c2 = 0 + 130 Reorder the terms: -130 + 130 + 4c + c2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + 4c + c2 = 0 + 130 4c + c2 = 0 + 130 Combine like terms: 0 + 130 = 130 4c + c2 = 130 The c term is 4c. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4c + 4 + c2 = 130 + 4 Reorder the terms: 4 + 4c + c2 = 130 + 4 Combine like terms: 130 + 4 = 134 4 + 4c + c2 = 134 Factor a perfect square on the left side: (c + 2)(c + 2) = 134 Calculate the square root of the right side: 11.575836903 Break this problem into two subproblems by setting (c + 2) equal to 11.575836903 and -11.575836903.Subproblem 1
c + 2 = 11.575836903 Simplifying c + 2 = 11.575836903 Reorder the terms: 2 + c = 11.575836903 Solving 2 + c = 11.575836903 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + c = 11.575836903 + -2 Combine like terms: 2 + -2 = 0 0 + c = 11.575836903 + -2 c = 11.575836903 + -2 Combine like terms: 11.575836903 + -2 = 9.575836903 c = 9.575836903 Simplifying c = 9.575836903Subproblem 2
c + 2 = -11.575836903 Simplifying c + 2 = -11.575836903 Reorder the terms: 2 + c = -11.575836903 Solving 2 + c = -11.575836903 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + c = -11.575836903 + -2 Combine like terms: 2 + -2 = 0 0 + c = -11.575836903 + -2 c = -11.575836903 + -2 Combine like terms: -11.575836903 + -2 = -13.575836903 c = -13.575836903 Simplifying c = -13.575836903Solution
The solution to the problem is based on the solutions from the subproblems. c = {9.575836903, -13.575836903}Solution
c = {9.575836903, -13.575836903}
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