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Simplifying x(600 + -1x) = 40000 (600 * x + -1x * x) = 40000 (600x + -1x2) = 40000 Solving 600x + -1x2 = 40000 Solving for variable 'x'. Reorder the terms: -40000 + 600x + -1x2 = 40000 + -40000 Combine like terms: 40000 + -40000 = 0 -40000 + 600x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 40000 + -600x + x2 = 0 Move the constant term to the right: Add '-40000' to each side of the equation. 40000 + -600x + -40000 + x2 = 0 + -40000 Reorder the terms: 40000 + -40000 + -600x + x2 = 0 + -40000 Combine like terms: 40000 + -40000 = 0 0 + -600x + x2 = 0 + -40000 -600x + x2 = 0 + -40000 Combine like terms: 0 + -40000 = -40000 -600x + x2 = -40000 The x term is -600x. Take half its coefficient (-300). Square it (90000) and add it to both sides. Add '90000' to each side of the equation. -600x + 90000 + x2 = -40000 + 90000 Reorder the terms: 90000 + -600x + x2 = -40000 + 90000 Combine like terms: -40000 + 90000 = 50000 90000 + -600x + x2 = 50000 Factor a perfect square on the left side: (x + -300)(x + -300) = 50000 Calculate the square root of the right side: 223.60679775 Break this problem into two subproblems by setting (x + -300) equal to 223.60679775 and -223.60679775.Subproblem 1
x + -300 = 223.60679775 Simplifying x + -300 = 223.60679775 Reorder the terms: -300 + x = 223.60679775 Solving -300 + x = 223.60679775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '300' to each side of the equation. -300 + 300 + x = 223.60679775 + 300 Combine like terms: -300 + 300 = 0 0 + x = 223.60679775 + 300 x = 223.60679775 + 300 Combine like terms: 223.60679775 + 300 = 523.60679775 x = 523.60679775 Simplifying x = 523.60679775Subproblem 2
x + -300 = -223.60679775 Simplifying x + -300 = -223.60679775 Reorder the terms: -300 + x = -223.60679775 Solving -300 + x = -223.60679775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '300' to each side of the equation. -300 + 300 + x = -223.60679775 + 300 Combine like terms: -300 + 300 = 0 0 + x = -223.60679775 + 300 x = -223.60679775 + 300 Combine like terms: -223.60679775 + 300 = 76.39320225 x = 76.39320225 Simplifying x = 76.39320225Solution
The solution to the problem is based on the solutions from the subproblems. x = {523.60679775, 76.39320225}
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