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Simplifying c2 + -5c + -366 = 0 Reorder the terms: -366 + -5c + c2 = 0 Solving -366 + -5c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '366' to each side of the equation. -366 + -5c + 366 + c2 = 0 + 366 Reorder the terms: -366 + 366 + -5c + c2 = 0 + 366 Combine like terms: -366 + 366 = 0 0 + -5c + c2 = 0 + 366 -5c + c2 = 0 + 366 Combine like terms: 0 + 366 = 366 -5c + c2 = 366 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 = 366 + 6.25 Reorder the terms: 6.25 + -5c + c2 = 366 + 6.25 Combine like terms: 366 + 6.25 = 372.25 6.25 + -5c + c2 = 372.25 Factor a perfect square on the left side: (c + -2.5)(c + -2.5) = 372.25 Calculate the square root of the right side: 19.293781382 Break this problem into two subproblems by setting (c + -2.5) equal to 19.293781382 and -19.293781382.Subproblem 1
c + -2.5 = 19.293781382 Simplifying c + -2.5 = 19.293781382 Reorder the terms: -2.5 + c = 19.293781382 Solving -2.5 + c = 19.293781382 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 = 19.293781382 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + c = 19.293781382 + 2.5 c = 19.293781382 + 2.5 Combine like terms: 19.293781382 + 2.5 = 21.793781382 c = 21.793781382 Simplifying c = 21.793781382Subproblem 2
c + -2.5 = -19.293781382 Simplifying c + -2.5 = -19.293781382 Reorder the terms: -2.5 + c = -19.293781382 Solving -2.5 + c = -19.293781382 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 = -19.293781382 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + c = -19.293781382 + 2.5 c = -19.293781382 + 2.5 Combine like terms: -19.293781382 + 2.5 = -16.793781382 c = -16.793781382 Simplifying c = -16.793781382Solution
The solution to the problem is based on the solutions from the subproblems. c = {21.793781382, -16.793781382}
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