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Simplifying c2 + -4c = 10 Reorder the terms: -4c + c2 = 10 Solving -4c + c2 = 10 Solving for variable 'c'. Reorder the terms: -10 + -4c + c2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -4c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -4c + 10 + c2 = 0 + 10 Reorder the terms: -10 + 10 + -4c + c2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -4c + c2 = 0 + 10 -4c + c2 = 0 + 10 Combine like terms: 0 + 10 = 10 -4c + c2 = 10 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 = 10 + 4 Reorder the terms: 4 + -4c + c2 = 10 + 4 Combine like terms: 10 + 4 = 14 4 + -4c + c2 = 14 Factor a perfect square on the left side: (c + -2)(c + -2) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (c + -2) equal to 3.741657387 and -3.741657387.Subproblem 1
c + -2 = 3.741657387 Simplifying c + -2 = 3.741657387 Reorder the terms: -2 + c = 3.741657387 Solving -2 + c = 3.741657387 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 = 3.741657387 + 2 Combine like terms: -2 + 2 = 0 0 + c = 3.741657387 + 2 c = 3.741657387 + 2 Combine like terms: 3.741657387 + 2 = 5.741657387 c = 5.741657387 Simplifying c = 5.741657387Subproblem 2
c + -2 = -3.741657387 Simplifying c + -2 = -3.741657387 Reorder the terms: -2 + c = -3.741657387 Solving -2 + c = -3.741657387 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 = -3.741657387 + 2 Combine like terms: -2 + 2 = 0 0 + c = -3.741657387 + 2 c = -3.741657387 + 2 Combine like terms: -3.741657387 + 2 = -1.741657387 c = -1.741657387 Simplifying c = -1.741657387Solution
The solution to the problem is based on the solutions from the subproblems. c = {5.741657387, -1.741657387}
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