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Simplifying x2 + -3160x + 1279000 = 0 Reorder the terms: 1279000 + -3160x + x2 = 0 Solving 1279000 + -3160x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1279000' to each side of the equation. 1279000 + -3160x + -1279000 + x2 = 0 + -1279000 Reorder the terms: 1279000 + -1279000 + -3160x + x2 = 0 + -1279000 Combine like terms: 1279000 + -1279000 = 0 0 + -3160x + x2 = 0 + -1279000 -3160x + x2 = 0 + -1279000 Combine like terms: 0 + -1279000 = -1279000 -3160x + x2 = -1279000 The x term is -3160x. Take half its coefficient (-1580). Square it (2496400) and add it to both sides. Add '2496400' to each side of the equation. -3160x + 2496400 + x2 = -1279000 + 2496400 Reorder the terms: 2496400 + -3160x + x2 = -1279000 + 2496400 Combine like terms: -1279000 + 2496400 = 1217400 2496400 + -3160x + x2 = 1217400 Factor a perfect square on the left side: (x + -1580)(x + -1580) = 1217400 Calculate the square root of the right side: 1103.35850928 Break this problem into two subproblems by setting (x + -1580) equal to 1103.35850928 and -1103.35850928.Subproblem 1
x + -1580 = 1103.35850928 Simplifying x + -1580 = 1103.35850928 Reorder the terms: -1580 + x = 1103.35850928 Solving -1580 + x = 1103.35850928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1580' to each side of the equation. -1580 + 1580 + x = 1103.35850928 + 1580 Combine like terms: -1580 + 1580 = 0 0 + x = 1103.35850928 + 1580 x = 1103.35850928 + 1580 Combine like terms: 1103.35850928 + 1580 = 2683.35850928 x = 2683.35850928 Simplifying x = 2683.35850928Subproblem 2
x + -1580 = -1103.35850928 Simplifying x + -1580 = -1103.35850928 Reorder the terms: -1580 + x = -1103.35850928 Solving -1580 + x = -1103.35850928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1580' to each side of the equation. -1580 + 1580 + x = -1103.35850928 + 1580 Combine like terms: -1580 + 1580 = 0 0 + x = -1103.35850928 + 1580 x = -1103.35850928 + 1580 Combine like terms: -1103.35850928 + 1580 = 476.64149072 x = 476.64149072 Simplifying x = 476.64149072Solution
The solution to the problem is based on the solutions from the subproblems. x = {2683.35850928, 476.64149072}
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