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Simplifying (c + -7)(c + -3) = 3 Reorder the terms: (-7 + c)(c + -3) = 3 Reorder the terms: (-7 + c)(-3 + c) = 3 Multiply (-7 + c) * (-3 + c) (-7(-3 + c) + c(-3 + c)) = 3 ((-3 * -7 + c * -7) + c(-3 + c)) = 3 ((21 + -7c) + c(-3 + c)) = 3 (21 + -7c + (-3 * c + c * c)) = 3 (21 + -7c + (-3c + c2)) = 3 Combine like terms: -7c + -3c = -10c (21 + -10c + c2) = 3 Solving 21 + -10c + c2 = 3 Solving for variable 'c'. Reorder the terms: 21 + -3 + -10c + c2 = 3 + -3 Combine like terms: 21 + -3 = 18 18 + -10c + c2 = 3 + -3 Combine like terms: 3 + -3 = 0 18 + -10c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -10c + -18 + c2 = 0 + -18 Reorder the terms: 18 + -18 + -10c + c2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -10c + c2 = 0 + -18 -10c + c2 = 0 + -18 Combine like terms: 0 + -18 = -18 -10c + c2 = -18 The c term is -10c. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10c + 25 + c2 = -18 + 25 Reorder the terms: 25 + -10c + c2 = -18 + 25 Combine like terms: -18 + 25 = 7 25 + -10c + c2 = 7 Factor a perfect square on the left side: (c + -5)(c + -5) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (c + -5) equal to 2.645751311 and -2.645751311.Subproblem 1
c + -5 = 2.645751311 Simplifying c + -5 = 2.645751311 Reorder the terms: -5 + c = 2.645751311 Solving -5 + c = 2.645751311 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + c = 2.645751311 + 5 Combine like terms: -5 + 5 = 0 0 + c = 2.645751311 + 5 c = 2.645751311 + 5 Combine like terms: 2.645751311 + 5 = 7.645751311 c = 7.645751311 Simplifying c = 7.645751311Subproblem 2
c + -5 = -2.645751311 Simplifying c + -5 = -2.645751311 Reorder the terms: -5 + c = -2.645751311 Solving -5 + c = -2.645751311 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + c = -2.645751311 + 5 Combine like terms: -5 + 5 = 0 0 + c = -2.645751311 + 5 c = -2.645751311 + 5 Combine like terms: -2.645751311 + 5 = 2.354248689 c = 2.354248689 Simplifying c = 2.354248689Solution
The solution to the problem is based on the solutions from the subproblems. c = {7.645751311, 2.354248689}
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