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Simplifying c2 + -24c + 82 = 0 Reorder the terms: 82 + -24c + c2 = 0 Solving 82 + -24c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '-82' to each side of the equation. 82 + -24c + -82 + c2 = 0 + -82 Reorder the terms: 82 + -82 + -24c + c2 = 0 + -82 Combine like terms: 82 + -82 = 0 0 + -24c + c2 = 0 + -82 -24c + c2 = 0 + -82 Combine like terms: 0 + -82 = -82 -24c + c2 = -82 The c term is -24c. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24c + 144 + c2 = -82 + 144 Reorder the terms: 144 + -24c + c2 = -82 + 144 Combine like terms: -82 + 144 = 62 144 + -24c + c2 = 62 Factor a perfect square on the left side: (c + -12)(c + -12) = 62 Calculate the square root of the right side: 7.874007874 Break this problem into two subproblems by setting (c + -12) equal to 7.874007874 and -7.874007874.Subproblem 1
c + -12 = 7.874007874 Simplifying c + -12 = 7.874007874 Reorder the terms: -12 + c = 7.874007874 Solving -12 + c = 7.874007874 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + c = 7.874007874 + 12 Combine like terms: -12 + 12 = 0 0 + c = 7.874007874 + 12 c = 7.874007874 + 12 Combine like terms: 7.874007874 + 12 = 19.874007874 c = 19.874007874 Simplifying c = 19.874007874Subproblem 2
c + -12 = -7.874007874 Simplifying c + -12 = -7.874007874 Reorder the terms: -12 + c = -7.874007874 Solving -12 + c = -7.874007874 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + c = -7.874007874 + 12 Combine like terms: -12 + 12 = 0 0 + c = -7.874007874 + 12 c = -7.874007874 + 12 Combine like terms: -7.874007874 + 12 = 4.125992126 c = 4.125992126 Simplifying c = 4.125992126Solution
The solution to the problem is based on the solutions from the subproblems. c = {19.874007874, 4.125992126}
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