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Simplifying 0 = 79000C + -1(1 + C2)(4.9)(88.96396) + -183 Reorder the terms for easier multiplication: 0 = 79000C + -1 * 4.9 * 88.96396(1 + C2) + -183 Multiply -1 * 4.9 0 = 79000C + -4.9 * 88.96396(1 + C2) + -183 Multiply -4.9 * 88.96396 0 = 79000C + -435.923404(1 + C2) + -183 0 = 79000C + (1 * -435.923404 + C2 * -435.923404) + -183 0 = 79000C + (-435.923404 + -435.923404C2) + -183 Reorder the terms: 0 = -435.923404 + -183 + 79000C + -435.923404C2 Combine like terms: -435.923404 + -183 = -618.923404 0 = -618.923404 + 79000C + -435.923404C2 Solving 0 = -618.923404 + 79000C + -435.923404C2 Solving for variable 'C'. Combine like terms: 0 + 618.923404 = 618.923404 618.923404 + -79000C + 435.923404C2 = -618.923404 + 79000C + -435.923404C2 + 618.923404 + -79000C + 435.923404C2 Reorder the terms: 618.923404 + -79000C + 435.923404C2 = -618.923404 + 618.923404 + 79000C + -79000C + -435.923404C2 + 435.923404C2 Combine like terms: -618.923404 + 618.923404 = 0.000000 618.923404 + -79000C + 435.923404C2 = 0.000000 + 79000C + -79000C + -435.923404C2 + 435.923404C2 618.923404 + -79000C + 435.923404C2 = 79000C + -79000C + -435.923404C2 + 435.923404C2 Combine like terms: 79000C + -79000C = 0 618.923404 + -79000C + 435.923404C2 = 0 + -435.923404C2 + 435.923404C2 618.923404 + -79000C + 435.923404C2 = -435.923404C2 + 435.923404C2 Combine like terms: -435.923404C2 + 435.923404C2 = 0.000000 618.923404 + -79000C + 435.923404C2 = 0.000000 Begin completing the square. Divide all terms by 435.923404 the coefficient of the squared term: Divide each side by '435.923404'. 1.41979852 + -181.2244979C + C2 = 0 Move the constant term to the right: Add '-1.41979852' to each side of the equation. 1.41979852 + -181.2244979C + -1.41979852 + C2 = 0 + -1.41979852 Reorder the terms: 1.41979852 + -1.41979852 + -181.2244979C + C2 = 0 + -1.41979852 Combine like terms: 1.41979852 + -1.41979852 = 0.00000000 0.00000000 + -181.2244979C + C2 = 0 + -1.41979852 -181.2244979C + C2 = 0 + -1.41979852 Combine like terms: 0 + -1.41979852 = -1.41979852 -181.2244979C + C2 = -1.41979852 The C term is -181.2244979C. Take half its coefficient (-90.61224895). Square it (8210.579660) and add it to both sides. Add '8210.579660' to each side of the equation. -181.2244979C + 8210.579660 + C2 = -1.41979852 + 8210.579660 Reorder the terms: 8210.579660 + -181.2244979C + C2 = -1.41979852 + 8210.579660 Combine like terms: -1.41979852 + 8210.579660 = 8209.15986148 8210.579660 + -181.2244979C + C2 = 8209.15986148 Factor a perfect square on the left side: (C + -90.61224895)(C + -90.61224895) = 8209.15986148 Calculate the square root of the right side: 90.604414139 Break this problem into two subproblems by setting (C + -90.61224895) equal to 90.604414139 and -90.604414139.Subproblem 1
C + -90.61224895 = 90.604414139 Simplifying C + -90.61224895 = 90.604414139 Reorder the terms: -90.61224895 + C = 90.604414139 Solving -90.61224895 + C = 90.604414139 Solving for variable 'C'. Move all terms containing C to the left, all other terms to the right. Add '90.61224895' to each side of the equation. -90.61224895 + 90.61224895 + C = 90.604414139 + 90.61224895 Combine like terms: -90.61224895 + 90.61224895 = 0.00000000 0.00000000 + C = 90.604414139 + 90.61224895 C = 90.604414139 + 90.61224895 Combine like terms: 90.604414139 + 90.61224895 = 181.216663089 C = 181.216663089 Simplifying C = 181.216663089Subproblem 2
C + -90.61224895 = -90.604414139 Simplifying C + -90.61224895 = -90.604414139 Reorder the terms: -90.61224895 + C = -90.604414139 Solving -90.61224895 + C = -90.604414139 Solving for variable 'C'. Move all terms containing C to the left, all other terms to the right. Add '90.61224895' to each side of the equation. -90.61224895 + 90.61224895 + C = -90.604414139 + 90.61224895 Combine like terms: -90.61224895 + 90.61224895 = 0.00000000 0.00000000 + C = -90.604414139 + 90.61224895 C = -90.604414139 + 90.61224895 Combine like terms: -90.604414139 + 90.61224895 = 0.007834811 C = 0.007834811 Simplifying C = 0.007834811Solution
The solution to the problem is based on the solutions from the subproblems. C = {181.216663089, 0.007834811}
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