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Simplifying -6c + c2 + 17 = 13 Reorder the terms: 17 + -6c + c2 = 13 Solving 17 + -6c + c2 = 13 Solving for variable 'c'. Reorder the terms: 17 + -13 + -6c + c2 = 13 + -13 Combine like terms: 17 + -13 = 4 4 + -6c + c2 = 13 + -13 Combine like terms: 13 + -13 = 0 4 + -6c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -6c + -4 + c2 = 0 + -4 Reorder the terms: 4 + -4 + -6c + c2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -6c + c2 = 0 + -4 -6c + c2 = 0 + -4 Combine like terms: 0 + -4 = -4 -6c + c2 = -4 The c term is -6c. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6c + 9 + c2 = -4 + 9 Reorder the terms: 9 + -6c + c2 = -4 + 9 Combine like terms: -4 + 9 = 5 9 + -6c + c2 = 5 Factor a perfect square on the left side: (c + -3)(c + -3) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (c + -3) equal to 2.236067978 and -2.236067978.Subproblem 1
c + -3 = 2.236067978 Simplifying c + -3 = 2.236067978 Reorder the terms: -3 + c = 2.236067978 Solving -3 + c = 2.236067978 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + c = 2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + c = 2.236067978 + 3 c = 2.236067978 + 3 Combine like terms: 2.236067978 + 3 = 5.236067978 c = 5.236067978 Simplifying c = 5.236067978Subproblem 2
c + -3 = -2.236067978 Simplifying c + -3 = -2.236067978 Reorder the terms: -3 + c = -2.236067978 Solving -3 + c = -2.236067978 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + c = -2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + c = -2.236067978 + 3 c = -2.236067978 + 3 Combine like terms: -2.236067978 + 3 = 0.763932022 c = 0.763932022 Simplifying c = 0.763932022Solution
The solution to the problem is based on the solutions from the subproblems. c = {5.236067978, 0.763932022}
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