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Simplifying c2 + 20c + -180 = 0 Reorder the terms: -180 + 20c + c2 = 0 Solving -180 + 20c + 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 + 20c + 180 + c2 = 0 + 180 Reorder the terms: -180 + 180 + 20c + c2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 20c + c2 = 0 + 180 20c + c2 = 0 + 180 Combine like terms: 0 + 180 = 180 20c + c2 = 180 The c term is 20c. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20c + 100 + c2 = 180 + 100 Reorder the terms: 100 + 20c + c2 = 180 + 100 Combine like terms: 180 + 100 = 280 100 + 20c + c2 = 280 Factor a perfect square on the left side: (c + 10)(c + 10) = 280 Calculate the square root of the right side: 16.733200531 Break this problem into two subproblems by setting (c + 10) equal to 16.733200531 and -16.733200531.Subproblem 1
c + 10 = 16.733200531 Simplifying c + 10 = 16.733200531 Reorder the terms: 10 + c = 16.733200531 Solving 10 + c = 16.733200531 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + c = 16.733200531 + -10 Combine like terms: 10 + -10 = 0 0 + c = 16.733200531 + -10 c = 16.733200531 + -10 Combine like terms: 16.733200531 + -10 = 6.733200531 c = 6.733200531 Simplifying c = 6.733200531Subproblem 2
c + 10 = -16.733200531 Simplifying c + 10 = -16.733200531 Reorder the terms: 10 + c = -16.733200531 Solving 10 + c = -16.733200531 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + c = -16.733200531 + -10 Combine like terms: 10 + -10 = 0 0 + c = -16.733200531 + -10 c = -16.733200531 + -10 Combine like terms: -16.733200531 + -10 = -26.733200531 c = -26.733200531 Simplifying c = -26.733200531Solution
The solution to the problem is based on the solutions from the subproblems. c = {6.733200531, -26.733200531}
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