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Simplifying 500000 = x(20 + -0.0002x) 500000 = (20 * x + -0.0002x * x) 500000 = (20x + -0.0002x2) Solving 500000 = 20x + -0.0002x2 Solving for variable 'x'. Reorder the terms: 500000 + -20x + 0.0002x2 = 20x + -20x + -0.0002x2 + 0.0002x2 Combine like terms: 20x + -20x = 0 500000 + -20x + 0.0002x2 = 0 + -0.0002x2 + 0.0002x2 500000 + -20x + 0.0002x2 = -0.0002x2 + 0.0002x2 Combine like terms: -0.0002x2 + 0.0002x2 = 0.0000 500000 + -20x + 0.0002x2 = 0.0000 Begin completing the square. Divide all terms by 0.0002 the coefficient of the squared term: Divide each side by '0.0002'. 2500000000 + -100000x + x2 = 0 Move the constant term to the right: Add '-2500000000' to each side of the equation. 2500000000 + -100000x + -2500000000 + x2 = 0 + -2500000000 Reorder the terms: 2500000000 + -2500000000 + -100000x + x2 = 0 + -2500000000 Combine like terms: 2500000000 + -2500000000 = 0 0 + -100000x + x2 = 0 + -2500000000 -100000x + x2 = 0 + -2500000000 Combine like terms: 0 + -2500000000 = -2500000000 -100000x + x2 = -2500000000 The x term is -100000x. Take half its coefficient (-50000). Square it (2500000000) and add it to both sides. Add '2500000000' to each side of the equation. -100000x + 2500000000 + x2 = -2500000000 + 2500000000 Reorder the terms: 2500000000 + -100000x + x2 = -2500000000 + 2500000000 Combine like terms: -2500000000 + 2500000000 = 0 2500000000 + -100000x + x2 = 0 Factor a perfect square on the left side: (x + -50000)(x + -50000) = 0 Calculate the square root of the right side: 0 Break this problem into two subproblems by setting (x + -50000) equal to 0 and 0.Subproblem 1
x + -50000 = 0 Simplifying x + -50000 = 0 Reorder the terms: -50000 + x = 0 Solving -50000 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50000' to each side of the equation. -50000 + 50000 + x = 0 + 50000 Combine like terms: -50000 + 50000 = 0 0 + x = 0 + 50000 x = 0 + 50000 Combine like terms: 0 + 50000 = 50000 x = 50000 Simplifying x = 50000Subproblem 2
x + -50000 = 0 Simplifying x + -50000 = 0 Reorder the terms: -50000 + x = 0 Solving -50000 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50000' to each side of the equation. -50000 + 50000 + x = 0 + 50000 Combine like terms: -50000 + 50000 = 0 0 + x = 0 + 50000 x = 0 + 50000 Combine like terms: 0 + 50000 = 50000 x = 50000 Simplifying x = 50000Solution
The solution to the problem is based on the solutions from the subproblems. x = {50000, 50000}
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