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Simplifying (c + -1)(c + 2) = 14 Reorder the terms: (-1 + c)(c + 2) = 14 Reorder the terms: (-1 + c)(2 + c) = 14 Multiply (-1 + c) * (2 + c) (-1(2 + c) + c(2 + c)) = 14 ((2 * -1 + c * -1) + c(2 + c)) = 14 ((-2 + -1c) + c(2 + c)) = 14 (-2 + -1c + (2 * c + c * c)) = 14 (-2 + -1c + (2c + c2)) = 14 Combine like terms: -1c + 2c = 1c (-2 + 1c + c2) = 14 Solving -2 + 1c + c2 = 14 Solving for variable 'c'. Reorder the terms: -2 + -14 + 1c + c2 = 14 + -14 Combine like terms: -2 + -14 = -16 -16 + 1c + c2 = 14 + -14 Combine like terms: 14 + -14 = 0 -16 + 1c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 1c + 16 + c2 = 0 + 16 Reorder the terms: -16 + 16 + 1c + c2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 1c + c2 = 0 + 16 1c + c2 = 0 + 16 Combine like terms: 0 + 16 = 16 1c + c2 = 16 The c term is 1c. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. c + 0.25 + c2 = 16 + 0.25 Reorder the terms: 0.25 + c + c2 = 16 + 0.25 Combine like terms: 16 + 0.25 = 16.25 0.25 + c + c2 = 16.25 Factor a perfect square on the left side: (c + 0.5)(c + 0.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (c + 0.5) equal to 4.031128874 and -4.031128874.Subproblem 1
c + 0.5 = 4.031128874 Simplifying c + 0.5 = 4.031128874 Reorder the terms: 0.5 + c = 4.031128874 Solving 0.5 + c = 4.031128874 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + c = 4.031128874 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + c = 4.031128874 + -0.5 c = 4.031128874 + -0.5 Combine like terms: 4.031128874 + -0.5 = 3.531128874 c = 3.531128874 Simplifying c = 3.531128874Subproblem 2
c + 0.5 = -4.031128874 Simplifying c + 0.5 = -4.031128874 Reorder the terms: 0.5 + c = -4.031128874 Solving 0.5 + c = -4.031128874 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + c = -4.031128874 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + c = -4.031128874 + -0.5 c = -4.031128874 + -0.5 Combine like terms: -4.031128874 + -0.5 = -4.531128874 c = -4.531128874 Simplifying c = -4.531128874Solution
The solution to the problem is based on the solutions from the subproblems. c = {3.531128874, -4.531128874}
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