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Simplifying 7.4644 + c2 + -3.8638c = 4 Reorder the terms: 7.4644 + -3.8638c + c2 = 4 Solving 7.4644 + -3.8638c + c2 = 4 Solving for variable 'c'. Reorder the terms: 7.4644 + -4 + -3.8638c + c2 = 4 + -4 Combine like terms: 7.4644 + -4 = 3.4644 3.4644 + -3.8638c + c2 = 4 + -4 Combine like terms: 4 + -4 = 0 3.4644 + -3.8638c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '-3.4644' to each side of the equation. 3.4644 + -3.8638c + -3.4644 + c2 = 0 + -3.4644 Reorder the terms: 3.4644 + -3.4644 + -3.8638c + c2 = 0 + -3.4644 Combine like terms: 3.4644 + -3.4644 = 0.0000 0.0000 + -3.8638c + c2 = 0 + -3.4644 -3.8638c + c2 = 0 + -3.4644 Combine like terms: 0 + -3.4644 = -3.4644 -3.8638c + c2 = -3.4644 The c term is -3.8638c. Take half its coefficient (-1.9319). Square it (3.73223761) and add it to both sides. Add '3.73223761' to each side of the equation. -3.8638c + 3.73223761 + c2 = -3.4644 + 3.73223761 Reorder the terms: 3.73223761 + -3.8638c + c2 = -3.4644 + 3.73223761 Combine like terms: -3.4644 + 3.73223761 = 0.26783761 3.73223761 + -3.8638c + c2 = 0.26783761 Factor a perfect square on the left side: (c + -1.9319)(c + -1.9319) = 0.26783761 Calculate the square root of the right side: 0.517530299 Break this problem into two subproblems by setting (c + -1.9319) equal to 0.517530299 and -0.517530299.Subproblem 1
c + -1.9319 = 0.517530299 Simplifying c + -1.9319 = 0.517530299 Reorder the terms: -1.9319 + c = 0.517530299 Solving -1.9319 + c = 0.517530299 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.9319' to each side of the equation. -1.9319 + 1.9319 + c = 0.517530299 + 1.9319 Combine like terms: -1.9319 + 1.9319 = 0.0000 0.0000 + c = 0.517530299 + 1.9319 c = 0.517530299 + 1.9319 Combine like terms: 0.517530299 + 1.9319 = 2.449430299 c = 2.449430299 Simplifying c = 2.449430299Subproblem 2
c + -1.9319 = -0.517530299 Simplifying c + -1.9319 = -0.517530299 Reorder the terms: -1.9319 + c = -0.517530299 Solving -1.9319 + c = -0.517530299 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.9319' to each side of the equation. -1.9319 + 1.9319 + c = -0.517530299 + 1.9319 Combine like terms: -1.9319 + 1.9319 = 0.0000 0.0000 + c = -0.517530299 + 1.9319 c = -0.517530299 + 1.9319 Combine like terms: -0.517530299 + 1.9319 = 1.414369701 c = 1.414369701 Simplifying c = 1.414369701Solution
The solution to the problem is based on the solutions from the subproblems. c = {2.449430299, 1.414369701}
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