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Simplifying c2 + -2c = 74 Reorder the terms: -2c + c2 = 74 Solving -2c + c2 = 74 Solving for variable 'c'. Reorder the terms: -74 + -2c + c2 = 74 + -74 Combine like terms: 74 + -74 = 0 -74 + -2c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '74' to each side of the equation. -74 + -2c + 74 + c2 = 0 + 74 Reorder the terms: -74 + 74 + -2c + c2 = 0 + 74 Combine like terms: -74 + 74 = 0 0 + -2c + c2 = 0 + 74 -2c + c2 = 0 + 74 Combine like terms: 0 + 74 = 74 -2c + c2 = 74 The c term is -2c. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2c + 1 + c2 = 74 + 1 Reorder the terms: 1 + -2c + c2 = 74 + 1 Combine like terms: 74 + 1 = 75 1 + -2c + c2 = 75 Factor a perfect square on the left side: (c + -1)(c + -1) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (c + -1) equal to 8.660254038 and -8.660254038.Subproblem 1
c + -1 = 8.660254038 Simplifying c + -1 = 8.660254038 Reorder the terms: -1 + c = 8.660254038 Solving -1 + c = 8.660254038 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + c = 8.660254038 + 1 Combine like terms: -1 + 1 = 0 0 + c = 8.660254038 + 1 c = 8.660254038 + 1 Combine like terms: 8.660254038 + 1 = 9.660254038 c = 9.660254038 Simplifying c = 9.660254038Subproblem 2
c + -1 = -8.660254038 Simplifying c + -1 = -8.660254038 Reorder the terms: -1 + c = -8.660254038 Solving -1 + c = -8.660254038 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + c = -8.660254038 + 1 Combine like terms: -1 + 1 = 0 0 + c = -8.660254038 + 1 c = -8.660254038 + 1 Combine like terms: -8.660254038 + 1 = -7.660254038 c = -7.660254038 Simplifying c = -7.660254038Solution
The solution to the problem is based on the solutions from the subproblems. c = {9.660254038, -7.660254038}
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