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Simplifying c2 + -4c + 1 = 0 Reorder the terms: 1 + -4c + c2 = 0 Solving 1 + -4c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -4c + -1 + c2 = 0 + -1 Reorder the terms: 1 + -1 + -4c + c2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4c + c2 = 0 + -1 -4c + c2 = 0 + -1 Combine like terms: 0 + -1 = -1 -4c + c2 = -1 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 = -1 + 4 Reorder the terms: 4 + -4c + c2 = -1 + 4 Combine like terms: -1 + 4 = 3 4 + -4c + c2 = 3 Factor a perfect square on the left side: (c + -2)(c + -2) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (c + -2) equal to 1.732050808 and -1.732050808.Subproblem 1
c + -2 = 1.732050808 Simplifying c + -2 = 1.732050808 Reorder the terms: -2 + c = 1.732050808 Solving -2 + c = 1.732050808 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 = 1.732050808 + 2 Combine like terms: -2 + 2 = 0 0 + c = 1.732050808 + 2 c = 1.732050808 + 2 Combine like terms: 1.732050808 + 2 = 3.732050808 c = 3.732050808 Simplifying c = 3.732050808Subproblem 2
c + -2 = -1.732050808 Simplifying c + -2 = -1.732050808 Reorder the terms: -2 + c = -1.732050808 Solving -2 + c = -1.732050808 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 = -1.732050808 + 2 Combine like terms: -2 + 2 = 0 0 + c = -1.732050808 + 2 c = -1.732050808 + 2 Combine like terms: -1.732050808 + 2 = 0.267949192 c = 0.267949192 Simplifying c = 0.267949192Solution
The solution to the problem is based on the solutions from the subproblems. c = {3.732050808, 0.267949192}
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