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Simplifying 4.36x2 + -240x + 2100 = 0 Reorder the terms: 2100 + -240x + 4.36x2 = 0 Solving 2100 + -240x + 4.36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.36 the coefficient of the squared term: Divide each side by '4.36'. 481.6513761 + -55.04587156x + x2 = 0 Move the constant term to the right: Add '-481.6513761' to each side of the equation. 481.6513761 + -55.04587156x + -481.6513761 + x2 = 0 + -481.6513761 Reorder the terms: 481.6513761 + -481.6513761 + -55.04587156x + x2 = 0 + -481.6513761 Combine like terms: 481.6513761 + -481.6513761 = 0.0000000 0.0000000 + -55.04587156x + x2 = 0 + -481.6513761 -55.04587156x + x2 = 0 + -481.6513761 Combine like terms: 0 + -481.6513761 = -481.6513761 -55.04587156x + x2 = -481.6513761 The x term is -55.04587156x. 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. -55.04587156x + 757.5119940 + x2 = -481.6513761 + 757.5119940 Reorder the terms: 757.5119940 + -55.04587156x + x2 = -481.6513761 + 757.5119940 Combine like terms: -481.6513761 + 757.5119940 = 275.8606179 757.5119940 + -55.04587156x + x2 = 275.8606179 Factor a perfect square on the left side: (x + -27.52293578)(x + -27.52293578) = 275.8606179 Calculate the square root of the right side: 16.609052288 Break this problem into two subproblems by setting (x + -27.52293578) equal to 16.609052288 and -16.609052288.Subproblem 1
x + -27.52293578 = 16.609052288 Simplifying x + -27.52293578 = 16.609052288 Reorder the terms: -27.52293578 + x = 16.609052288 Solving -27.52293578 + x = 16.609052288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.52293578' to each side of the equation. -27.52293578 + 27.52293578 + x = 16.609052288 + 27.52293578 Combine like terms: -27.52293578 + 27.52293578 = 0.00000000 0.00000000 + x = 16.609052288 + 27.52293578 x = 16.609052288 + 27.52293578 Combine like terms: 16.609052288 + 27.52293578 = 44.131988068 x = 44.131988068 Simplifying x = 44.131988068Subproblem 2
x + -27.52293578 = -16.609052288 Simplifying x + -27.52293578 = -16.609052288 Reorder the terms: -27.52293578 + x = -16.609052288 Solving -27.52293578 + x = -16.609052288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.52293578' to each side of the equation. -27.52293578 + 27.52293578 + x = -16.609052288 + 27.52293578 Combine like terms: -27.52293578 + 27.52293578 = 0.00000000 0.00000000 + x = -16.609052288 + 27.52293578 x = -16.609052288 + 27.52293578 Combine like terms: -16.609052288 + 27.52293578 = 10.913883492 x = 10.913883492 Simplifying x = 10.913883492Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.131988068, 10.913883492}
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