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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 = 132.575241993 x = 132.575241993 Simplifying x = 132.575241993Subproblem 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 = -980.575241993 x = -980.575241993 Simplifying x = -980.575241993Solution
The solution to the problem is based on the solutions from the subproblems. x = {132.575241993, -980.575241993}
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