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Simplifying 61631 = 4c2 + 1490c Reorder the terms: 61631 = 1490c + 4c2 Solving 61631 = 1490c + 4c2 Solving for variable 'c'. Reorder the terms: 61631 + -1490c + -4c2 = 1490c + -1490c + 4c2 + -4c2 Combine like terms: 1490c + -1490c = 0 61631 + -1490c + -4c2 = 0 + 4c2 + -4c2 61631 + -1490c + -4c2 = 4c2 + -4c2 Combine like terms: 4c2 + -4c2 = 0 61631 + -1490c + -4c2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -15407.75 + 372.5c + c2 = 0 Move the constant term to the right: Add '15407.75' to each side of the equation. -15407.75 + 372.5c + 15407.75 + c2 = 0 + 15407.75 Reorder the terms: -15407.75 + 15407.75 + 372.5c + c2 = 0 + 15407.75 Combine like terms: -15407.75 + 15407.75 = 0.00 0.00 + 372.5c + c2 = 0 + 15407.75 372.5c + c2 = 0 + 15407.75 Combine like terms: 0 + 15407.75 = 15407.75 372.5c + c2 = 15407.75 The c term is 372.5c. Take half its coefficient (186.25). Square it (34689.0625) and add it to both sides. Add '34689.0625' to each side of the equation. 372.5c + 34689.0625 + c2 = 15407.75 + 34689.0625 Reorder the terms: 34689.0625 + 372.5c + c2 = 15407.75 + 34689.0625 Combine like terms: 15407.75 + 34689.0625 = 50096.8125 34689.0625 + 372.5c + c2 = 50096.8125 Factor a perfect square on the left side: (c + 186.25)(c + 186.25) = 50096.8125 Calculate the square root of the right side: 223.823172393 Break this problem into two subproblems by setting (c + 186.25) equal to 223.823172393 and -223.823172393.Subproblem 1
c + 186.25 = 223.823172393 Simplifying c + 186.25 = 223.823172393 Reorder the terms: 186.25 + c = 223.823172393 Solving 186.25 + c = 223.823172393 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-186.25' to each side of the equation. 186.25 + -186.25 + c = 223.823172393 + -186.25 Combine like terms: 186.25 + -186.25 = 0.00 0.00 + c = 223.823172393 + -186.25 c = 223.823172393 + -186.25 Combine like terms: 223.823172393 + -186.25 = 37.573172393 c = 37.573172393 Simplifying c = 37.573172393Subproblem 2
c + 186.25 = -223.823172393 Simplifying c + 186.25 = -223.823172393 Reorder the terms: 186.25 + c = -223.823172393 Solving 186.25 + c = -223.823172393 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-186.25' to each side of the equation. 186.25 + -186.25 + c = -223.823172393 + -186.25 Combine like terms: 186.25 + -186.25 = 0.00 0.00 + c = -223.823172393 + -186.25 c = -223.823172393 + -186.25 Combine like terms: -223.823172393 + -186.25 = -410.073172393 c = -410.073172393 Simplifying c = -410.073172393Solution
The solution to the problem is based on the solutions from the subproblems. c = {37.573172393, -410.073172393}
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