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Simplifying 60 = 41x + -5.5x2 Solving 60 = 41x + -5.5x2 Solving for variable 'x'. Reorder the terms: 60 + -41x + 5.5x2 = 41x + -41x + -5.5x2 + 5.5x2 Combine like terms: 41x + -41x = 0 60 + -41x + 5.5x2 = 0 + -5.5x2 + 5.5x2 60 + -41x + 5.5x2 = -5.5x2 + 5.5x2 Combine like terms: -5.5x2 + 5.5x2 = 0.0 60 + -41x + 5.5x2 = 0.0 Begin completing the square. Divide all terms by 5.5 the coefficient of the squared term: Divide each side by '5.5'. 10.90909091 + -7.454545455x + x2 = 0 Move the constant term to the right: Add '-10.90909091' to each side of the equation. 10.90909091 + -7.454545455x + -10.90909091 + x2 = 0 + -10.90909091 Reorder the terms: 10.90909091 + -10.90909091 + -7.454545455x + x2 = 0 + -10.90909091 Combine like terms: 10.90909091 + -10.90909091 = 0.00000000 0.00000000 + -7.454545455x + x2 = 0 + -10.90909091 -7.454545455x + x2 = 0 + -10.90909091 Combine like terms: 0 + -10.90909091 = -10.90909091 -7.454545455x + x2 = -10.90909091 The x term is -7.454545455x. Take half its coefficient (-3.727272728). Square it (13.89256199) and add it to both sides. Add '13.89256199' to each side of the equation. -7.454545455x + 13.89256199 + x2 = -10.90909091 + 13.89256199 Reorder the terms: 13.89256199 + -7.454545455x + x2 = -10.90909091 + 13.89256199 Combine like terms: -10.90909091 + 13.89256199 = 2.98347108 13.89256199 + -7.454545455x + x2 = 2.98347108 Factor a perfect square on the left side: (x + -3.727272728)(x + -3.727272728) = 2.98347108 Calculate the square root of the right side: 1.727272729 Break this problem into two subproblems by setting (x + -3.727272728) equal to 1.727272729 and -1.727272729.Subproblem 1
x + -3.727272728 = 1.727272729 Simplifying x + -3.727272728 = 1.727272729 Reorder the terms: -3.727272728 + x = 1.727272729 Solving -3.727272728 + x = 1.727272729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.727272728' to each side of the equation. -3.727272728 + 3.727272728 + x = 1.727272729 + 3.727272728 Combine like terms: -3.727272728 + 3.727272728 = 0.000000000 0.000000000 + x = 1.727272729 + 3.727272728 x = 1.727272729 + 3.727272728 Combine like terms: 1.727272729 + 3.727272728 = 5.454545457 x = 5.454545457 Simplifying x = 5.454545457Subproblem 2
x + -3.727272728 = -1.727272729 Simplifying x + -3.727272728 = -1.727272729 Reorder the terms: -3.727272728 + x = -1.727272729 Solving -3.727272728 + x = -1.727272729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.727272728' to each side of the equation. -3.727272728 + 3.727272728 + x = -1.727272729 + 3.727272728 Combine like terms: -3.727272728 + 3.727272728 = 0.000000000 0.000000000 + x = -1.727272729 + 3.727272728 x = -1.727272729 + 3.727272728 Combine like terms: -1.727272729 + 3.727272728 = 1.999999999 x = 1.999999999 Simplifying x = 1.999999999Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.454545457, 1.999999999}
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