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Simplifying c2 + 4c + -20 = 180 Reorder the terms: -20 + 4c + c2 = 180 Solving -20 + 4c + c2 = 180 Solving for variable 'c'. Reorder the terms: -20 + -180 + 4c + c2 = 180 + -180 Combine like terms: -20 + -180 = -200 -200 + 4c + c2 = 180 + -180 Combine like terms: 180 + -180 = 0 -200 + 4c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '200' to each side of the equation. -200 + 4c + 200 + c2 = 0 + 200 Reorder the terms: -200 + 200 + 4c + c2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 4c + c2 = 0 + 200 4c + c2 = 0 + 200 Combine like terms: 0 + 200 = 200 4c + c2 = 200 The c term is 4c. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4c + 4 + c2 = 200 + 4 Reorder the terms: 4 + 4c + c2 = 200 + 4 Combine like terms: 200 + 4 = 204 4 + 4c + c2 = 204 Factor a perfect square on the left side: (c + 2)(c + 2) = 204 Calculate the square root of the right side: 14.282856857 Break this problem into two subproblems by setting (c + 2) equal to 14.282856857 and -14.282856857.Subproblem 1
c + 2 = 14.282856857 Simplifying c + 2 = 14.282856857 Reorder the terms: 2 + c = 14.282856857 Solving 2 + c = 14.282856857 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + c = 14.282856857 + -2 Combine like terms: 2 + -2 = 0 0 + c = 14.282856857 + -2 c = 14.282856857 + -2 Combine like terms: 14.282856857 + -2 = 12.282856857 c = 12.282856857 Simplifying c = 12.282856857Subproblem 2
c + 2 = -14.282856857 Simplifying c + 2 = -14.282856857 Reorder the terms: 2 + c = -14.282856857 Solving 2 + c = -14.282856857 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + c = -14.282856857 + -2 Combine like terms: 2 + -2 = 0 0 + c = -14.282856857 + -2 c = -14.282856857 + -2 Combine like terms: -14.282856857 + -2 = -16.282856857 c = -16.282856857 Simplifying c = -16.282856857Solution
The solution to the problem is based on the solutions from the subproblems. c = {12.282856857, -16.282856857}
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