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Simplifying x2 + -800x = -140000 Reorder the terms: -800x + x2 = -140000 Solving -800x + x2 = -140000 Solving for variable 'x'. Reorder the terms: 140000 + -800x + x2 = -140000 + 140000 Combine like terms: -140000 + 140000 = 0 140000 + -800x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-140000' to each side of the equation. 140000 + -800x + -140000 + x2 = 0 + -140000 Reorder the terms: 140000 + -140000 + -800x + x2 = 0 + -140000 Combine like terms: 140000 + -140000 = 0 0 + -800x + x2 = 0 + -140000 -800x + x2 = 0 + -140000 Combine like terms: 0 + -140000 = -140000 -800x + x2 = -140000 The x term is -800x. Take half its coefficient (-400). Square it (160000) and add it to both sides. Add '160000' to each side of the equation. -800x + 160000 + x2 = -140000 + 160000 Reorder the terms: 160000 + -800x + x2 = -140000 + 160000 Combine like terms: -140000 + 160000 = 20000 160000 + -800x + x2 = 20000 Factor a perfect square on the left side: (x + -400)(x + -400) = 20000 Calculate the square root of the right side: 141.421356237 Break this problem into two subproblems by setting (x + -400) equal to 141.421356237 and -141.421356237.Subproblem 1
x + -400 = 141.421356237 Simplifying x + -400 = 141.421356237 Reorder the terms: -400 + x = 141.421356237 Solving -400 + x = 141.421356237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '400' to each side of the equation. -400 + 400 + x = 141.421356237 + 400 Combine like terms: -400 + 400 = 0 0 + x = 141.421356237 + 400 x = 141.421356237 + 400 Combine like terms: 141.421356237 + 400 = 541.421356237 x = 541.421356237 Simplifying x = 541.421356237Subproblem 2
x + -400 = -141.421356237 Simplifying x + -400 = -141.421356237 Reorder the terms: -400 + x = -141.421356237 Solving -400 + x = -141.421356237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '400' to each side of the equation. -400 + 400 + x = -141.421356237 + 400 Combine like terms: -400 + 400 = 0 0 + x = -141.421356237 + 400 x = -141.421356237 + 400 Combine like terms: -141.421356237 + 400 = 258.578643763 x = 258.578643763 Simplifying x = 258.578643763Solution
The solution to the problem is based on the solutions from the subproblems. x = {541.421356237, 258.578643763}
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