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Simplifying x2 + -848x = 130000 Reorder the terms: -848x + x2 = 130000 Solving -848x + x2 = 130000 Solving for variable 'x'. Reorder the terms: -130000 + -848x + x2 = 130000 + -130000 Combine like terms: 130000 + -130000 = 0 -130000 + -848x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '130000' to each side of the equation. -130000 + -848x + 130000 + x2 = 0 + 130000 Reorder the terms: -130000 + 130000 + -848x + x2 = 0 + 130000 Combine like terms: -130000 + 130000 = 0 0 + -848x + x2 = 0 + 130000 -848x + x2 = 0 + 130000 Combine like terms: 0 + 130000 = 130000 -848x + x2 = 130000 The x term is -848x. Take half its coefficient (-424). Square it (179776) and add it to both sides. Add '179776' to each side of the equation. -848x + 179776 + x2 = 130000 + 179776 Reorder the terms: 179776 + -848x + x2 = 130000 + 179776 Combine like terms: 130000 + 179776 = 309776 179776 + -848x + x2 = 309776 Factor a perfect square on the left side: (x + -424)(x + -424) = 309776 Calculate the square root of the right side: 556.575241993 Break this problem into two subproblems by setting (x + -424) equal to 556.575241993 and -556.575241993.Subproblem 1
x + -424 = 556.575241993 Simplifying x + -424 = 556.575241993 Reorder the terms: -424 + x = 556.575241993 Solving -424 + x = 556.575241993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '424' to each side of the equation. -424 + 424 + x = 556.575241993 + 424 Combine like terms: -424 + 424 = 0 0 + x = 556.575241993 + 424 x = 556.575241993 + 424 Combine like terms: 556.575241993 + 424 = 980.575241993 x = 980.575241993 Simplifying x = 980.575241993Subproblem 2
x + -424 = -556.575241993 Simplifying x + -424 = -556.575241993 Reorder the terms: -424 + x = -556.575241993 Solving -424 + x = -556.575241993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '424' to each side of the equation. -424 + 424 + x = -556.575241993 + 424 Combine like terms: -424 + 424 = 0 0 + x = -556.575241993 + 424 x = -556.575241993 + 424 Combine like terms: -556.575241993 + 424 = -132.575241993 x = -132.575241993 Simplifying x = -132.575241993Solution
The solution to the problem is based on the solutions from the subproblems. x = {980.575241993, -132.575241993}
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