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Simplifying c2 + 19c + -180 = 0 Reorder the terms: -180 + 19c + c2 = 0 Solving -180 + 19c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + 19c + 180 + c2 = 0 + 180 Reorder the terms: -180 + 180 + 19c + c2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 19c + c2 = 0 + 180 19c + c2 = 0 + 180 Combine like terms: 0 + 180 = 180 19c + c2 = 180 The c term is 19c. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19c + 90.25 + c2 = 180 + 90.25 Reorder the terms: 90.25 + 19c + c2 = 180 + 90.25 Combine like terms: 180 + 90.25 = 270.25 90.25 + 19c + c2 = 270.25 Factor a perfect square on the left side: (c + 9.5)(c + 9.5) = 270.25 Calculate the square root of the right side: 16.439282223 Break this problem into two subproblems by setting (c + 9.5) equal to 16.439282223 and -16.439282223.Subproblem 1
c + 9.5 = 16.439282223 Simplifying c + 9.5 = 16.439282223 Reorder the terms: 9.5 + c = 16.439282223 Solving 9.5 + c = 16.439282223 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + c = 16.439282223 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + c = 16.439282223 + -9.5 c = 16.439282223 + -9.5 Combine like terms: 16.439282223 + -9.5 = 6.939282223 c = 6.939282223 Simplifying c = 6.939282223Subproblem 2
c + 9.5 = -16.439282223 Simplifying c + 9.5 = -16.439282223 Reorder the terms: 9.5 + c = -16.439282223 Solving 9.5 + c = -16.439282223 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + c = -16.439282223 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + c = -16.439282223 + -9.5 c = -16.439282223 + -9.5 Combine like terms: -16.439282223 + -9.5 = -25.939282223 c = -25.939282223 Simplifying c = -25.939282223Solution
The solution to the problem is based on the solutions from the subproblems. c = {6.939282223, -25.939282223}
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