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Simplifying x2 + -2000x + 440000 = 0 Reorder the terms: 440000 + -2000x + x2 = 0 Solving 440000 + -2000x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-440000' to each side of the equation. 440000 + -2000x + -440000 + x2 = 0 + -440000 Reorder the terms: 440000 + -440000 + -2000x + x2 = 0 + -440000 Combine like terms: 440000 + -440000 = 0 0 + -2000x + x2 = 0 + -440000 -2000x + x2 = 0 + -440000 Combine like terms: 0 + -440000 = -440000 -2000x + x2 = -440000 The x term is -2000x. Take half its coefficient (-1000). Square it (1000000) and add it to both sides. Add '1000000' to each side of the equation. -2000x + 1000000 + x2 = -440000 + 1000000 Reorder the terms: 1000000 + -2000x + x2 = -440000 + 1000000 Combine like terms: -440000 + 1000000 = 560000 1000000 + -2000x + x2 = 560000 Factor a perfect square on the left side: (x + -1000)(x + -1000) = 560000 Calculate the square root of the right side: 748.331477355 Break this problem into two subproblems by setting (x + -1000) equal to 748.331477355 and -748.331477355.Subproblem 1
x + -1000 = 748.331477355 Simplifying x + -1000 = 748.331477355 Reorder the terms: -1000 + x = 748.331477355 Solving -1000 + x = 748.331477355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1000' to each side of the equation. -1000 + 1000 + x = 748.331477355 + 1000 Combine like terms: -1000 + 1000 = 0 0 + x = 748.331477355 + 1000 x = 748.331477355 + 1000 Combine like terms: 748.331477355 + 1000 = 1748.331477355 x = 1748.331477355 Simplifying x = 1748.331477355Subproblem 2
x + -1000 = -748.331477355 Simplifying x + -1000 = -748.331477355 Reorder the terms: -1000 + x = -748.331477355 Solving -1000 + x = -748.331477355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1000' to each side of the equation. -1000 + 1000 + x = -748.331477355 + 1000 Combine like terms: -1000 + 1000 = 0 0 + x = -748.331477355 + 1000 x = -748.331477355 + 1000 Combine like terms: -748.331477355 + 1000 = 251.668522645 x = 251.668522645 Simplifying x = 251.668522645Solution
The solution to the problem is based on the solutions from the subproblems. x = {1748.331477355, 251.668522645}
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