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Simplifying 4.36u2 + -240u + 2100 = 0 Reorder the terms: 2100 + -240u + 4.36u2 = 0 Solving 2100 + -240u + 4.36u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 4.36 the coefficient of the squared term: Divide each side by '4.36'. 481.6513761 + -55.04587156u + u2 = 0 Move the constant term to the right: Add '-481.6513761' to each side of the equation. 481.6513761 + -55.04587156u + -481.6513761 + u2 = 0 + -481.6513761 Reorder the terms: 481.6513761 + -481.6513761 + -55.04587156u + u2 = 0 + -481.6513761 Combine like terms: 481.6513761 + -481.6513761 = 0.0000000 0.0000000 + -55.04587156u + u2 = 0 + -481.6513761 -55.04587156u + u2 = 0 + -481.6513761 Combine like terms: 0 + -481.6513761 = -481.6513761 -55.04587156u + u2 = -481.6513761 The u term is -55.04587156u. Take half its coefficient (-27.52293578). Square it (757.5119940) and add it to both sides. Add '757.5119940' to each side of the equation. -55.04587156u + 757.5119940 + u2 = -481.6513761 + 757.5119940 Reorder the terms: 757.5119940 + -55.04587156u + u2 = -481.6513761 + 757.5119940 Combine like terms: -481.6513761 + 757.5119940 = 275.8606179 757.5119940 + -55.04587156u + u2 = 275.8606179 Factor a perfect square on the left side: (u + -27.52293578)(u + -27.52293578) = 275.8606179 Calculate the square root of the right side: 16.609052288 Break this problem into two subproblems by setting (u + -27.52293578) equal to 16.609052288 and -16.609052288.Subproblem 1
u + -27.52293578 = 16.609052288 Simplifying u + -27.52293578 = 16.609052288 Reorder the terms: -27.52293578 + u = 16.609052288 Solving -27.52293578 + u = 16.609052288 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '27.52293578' to each side of the equation. -27.52293578 + 27.52293578 + u = 16.609052288 + 27.52293578 Combine like terms: -27.52293578 + 27.52293578 = 0.00000000 0.00000000 + u = 16.609052288 + 27.52293578 u = 16.609052288 + 27.52293578 Combine like terms: 16.609052288 + 27.52293578 = 44.131988068 u = 44.131988068 Simplifying u = 44.131988068Subproblem 2
u + -27.52293578 = -16.609052288 Simplifying u + -27.52293578 = -16.609052288 Reorder the terms: -27.52293578 + u = -16.609052288 Solving -27.52293578 + u = -16.609052288 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '27.52293578' to each side of the equation. -27.52293578 + 27.52293578 + u = -16.609052288 + 27.52293578 Combine like terms: -27.52293578 + 27.52293578 = 0.00000000 0.00000000 + u = -16.609052288 + 27.52293578 u = -16.609052288 + 27.52293578 Combine like terms: -16.609052288 + 27.52293578 = 10.913883492 u = 10.913883492 Simplifying u = 10.913883492Solution
The solution to the problem is based on the solutions from the subproblems. u = {44.131988068, 10.913883492}
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