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Simplifying 0 = -1x2 + 2400x + -1240000 Reorder the terms: 0 = -1240000 + 2400x + -1x2 Solving 0 = -1240000 + 2400x + -1x2 Solving for variable 'x'. Combine like terms: 0 + 1240000 = 1240000 1240000 + -2400x + x2 = -1240000 + 2400x + -1x2 + 1240000 + -2400x + x2 Reorder the terms: 1240000 + -2400x + x2 = -1240000 + 1240000 + 2400x + -2400x + -1x2 + x2 Combine like terms: -1240000 + 1240000 = 0 1240000 + -2400x + x2 = 0 + 2400x + -2400x + -1x2 + x2 1240000 + -2400x + x2 = 2400x + -2400x + -1x2 + x2 Combine like terms: 2400x + -2400x = 0 1240000 + -2400x + x2 = 0 + -1x2 + x2 1240000 + -2400x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 1240000 + -2400x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1240000' to each side of the equation. 1240000 + -2400x + -1240000 + x2 = 0 + -1240000 Reorder the terms: 1240000 + -1240000 + -2400x + x2 = 0 + -1240000 Combine like terms: 1240000 + -1240000 = 0 0 + -2400x + x2 = 0 + -1240000 -2400x + x2 = 0 + -1240000 Combine like terms: 0 + -1240000 = -1240000 -2400x + x2 = -1240000 The x term is -2400x. Take half its coefficient (-1200). Square it (1440000) and add it to both sides. Add '1440000' to each side of the equation. -2400x + 1440000 + x2 = -1240000 + 1440000 Reorder the terms: 1440000 + -2400x + x2 = -1240000 + 1440000 Combine like terms: -1240000 + 1440000 = 200000 1440000 + -2400x + x2 = 200000 Factor a perfect square on the left side: (x + -1200)(x + -1200) = 200000 Calculate the square root of the right side: 447.2135955 Break this problem into two subproblems by setting (x + -1200) equal to 447.2135955 and -447.2135955.Subproblem 1
x + -1200 = 447.2135955 Simplifying x + -1200 = 447.2135955 Reorder the terms: -1200 + x = 447.2135955 Solving -1200 + x = 447.2135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1200' to each side of the equation. -1200 + 1200 + x = 447.2135955 + 1200 Combine like terms: -1200 + 1200 = 0 0 + x = 447.2135955 + 1200 x = 447.2135955 + 1200 Combine like terms: 447.2135955 + 1200 = 1647.2135955 x = 1647.2135955 Simplifying x = 1647.2135955Subproblem 2
x + -1200 = -447.2135955 Simplifying x + -1200 = -447.2135955 Reorder the terms: -1200 + x = -447.2135955 Solving -1200 + x = -447.2135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1200' to each side of the equation. -1200 + 1200 + x = -447.2135955 + 1200 Combine like terms: -1200 + 1200 = 0 0 + x = -447.2135955 + 1200 x = -447.2135955 + 1200 Combine like terms: -447.2135955 + 1200 = 752.7864045 x = 752.7864045 Simplifying x = 752.7864045Solution
The solution to the problem is based on the solutions from the subproblems. x = {1647.2135955, 752.7864045}
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