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Simplifying 6 = 0.01x(120 + -1x) 6 = (120 * 0.01x + -1x * 0.01x) 6 = (1.2x + -0.01x2) Solving 6 = 1.2x + -0.01x2 Solving for variable 'x'. Reorder the terms: 6 + -1.2x + 0.01x2 = 1.2x + -1.2x + -0.01x2 + 0.01x2 Combine like terms: 1.2x + -1.2x = 0.0 6 + -1.2x + 0.01x2 = 0.0 + -0.01x2 + 0.01x2 6 + -1.2x + 0.01x2 = -0.01x2 + 0.01x2 Combine like terms: -0.01x2 + 0.01x2 = 0.00 6 + -1.2x + 0.01x2 = 0.00 Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. 600 + -120x + x2 = 0 Move the constant term to the right: Add '-600' to each side of the equation. 600 + -120x + -600 + x2 = 0 + -600 Reorder the terms: 600 + -600 + -120x + x2 = 0 + -600 Combine like terms: 600 + -600 = 0 0 + -120x + x2 = 0 + -600 -120x + x2 = 0 + -600 Combine like terms: 0 + -600 = -600 -120x + x2 = -600 The x term is -120x. Take half its coefficient (-60). Square it (3600) and add it to both sides. Add '3600' to each side of the equation. -120x + 3600 + x2 = -600 + 3600 Reorder the terms: 3600 + -120x + x2 = -600 + 3600 Combine like terms: -600 + 3600 = 3000 3600 + -120x + x2 = 3000 Factor a perfect square on the left side: (x + -60)(x + -60) = 3000 Calculate the square root of the right side: 54.772255751 Break this problem into two subproblems by setting (x + -60) equal to 54.772255751 and -54.772255751.Subproblem 1
x + -60 = 54.772255751 Simplifying x + -60 = 54.772255751 Reorder the terms: -60 + x = 54.772255751 Solving -60 + x = 54.772255751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + x = 54.772255751 + 60 Combine like terms: -60 + 60 = 0 0 + x = 54.772255751 + 60 x = 54.772255751 + 60 Combine like terms: 54.772255751 + 60 = 114.772255751 x = 114.772255751 Simplifying x = 114.772255751Subproblem 2
x + -60 = -54.772255751 Simplifying x + -60 = -54.772255751 Reorder the terms: -60 + x = -54.772255751 Solving -60 + x = -54.772255751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + x = -54.772255751 + 60 Combine like terms: -60 + 60 = 0 0 + x = -54.772255751 + 60 x = -54.772255751 + 60 Combine like terms: -54.772255751 + 60 = 5.227744249 x = 5.227744249 Simplifying x = 5.227744249Solution
The solution to the problem is based on the solutions from the subproblems. x = {114.772255751, 5.227744249}
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