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Simplifying 4c2 + 1773.8c + -151666.67 = 0 Reorder the terms: -151666.67 + 1773.8c + 4c2 = 0 Solving -151666.67 + 1773.8c + 4c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -37916.6675 + 443.45c + c2 = 0 Move the constant term to the right: Add '37916.6675' to each side of the equation. -37916.6675 + 443.45c + 37916.6675 + c2 = 0 + 37916.6675 Reorder the terms: -37916.6675 + 37916.6675 + 443.45c + c2 = 0 + 37916.6675 Combine like terms: -37916.6675 + 37916.6675 = 0.0000 0.0000 + 443.45c + c2 = 0 + 37916.6675 443.45c + c2 = 0 + 37916.6675 Combine like terms: 0 + 37916.6675 = 37916.6675 443.45c + c2 = 37916.6675 The c term is 443.45c. Take half its coefficient (221.725). Square it (49161.97563) and add it to both sides. Add '49161.97563' to each side of the equation. 443.45c + 49161.97563 + c2 = 37916.6675 + 49161.97563 Reorder the terms: 49161.97563 + 443.45c + c2 = 37916.6675 + 49161.97563 Combine like terms: 37916.6675 + 49161.97563 = 87078.64313 49161.97563 + 443.45c + c2 = 87078.64313 Factor a perfect square on the left side: (c + 221.725)(c + 221.725) = 87078.64313 Calculate the square root of the right side: 295.090906553 Break this problem into two subproblems by setting (c + 221.725) equal to 295.090906553 and -295.090906553.Subproblem 1
c + 221.725 = 295.090906553 Simplifying c + 221.725 = 295.090906553 Reorder the terms: 221.725 + c = 295.090906553 Solving 221.725 + c = 295.090906553 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-221.725' to each side of the equation. 221.725 + -221.725 + c = 295.090906553 + -221.725 Combine like terms: 221.725 + -221.725 = 0.000 0.000 + c = 295.090906553 + -221.725 c = 295.090906553 + -221.725 Combine like terms: 295.090906553 + -221.725 = 73.365906553 c = 73.365906553 Simplifying c = 73.365906553Subproblem 2
c + 221.725 = -295.090906553 Simplifying c + 221.725 = -295.090906553 Reorder the terms: 221.725 + c = -295.090906553 Solving 221.725 + c = -295.090906553 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-221.725' to each side of the equation. 221.725 + -221.725 + c = -295.090906553 + -221.725 Combine like terms: 221.725 + -221.725 = 0.000 0.000 + c = -295.090906553 + -221.725 c = -295.090906553 + -221.725 Combine like terms: -295.090906553 + -221.725 = -516.815906553 c = -516.815906553 Simplifying c = -516.815906553Solution
The solution to the problem is based on the solutions from the subproblems. c = {73.365906553, -516.815906553}
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