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Simplifying x2 + -2100x + 100000 = 0 Reorder the terms: 100000 + -2100x + x2 = 0 Solving 100000 + -2100x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-100000' to each side of the equation. 100000 + -2100x + -100000 + x2 = 0 + -100000 Reorder the terms: 100000 + -100000 + -2100x + x2 = 0 + -100000 Combine like terms: 100000 + -100000 = 0 0 + -2100x + x2 = 0 + -100000 -2100x + x2 = 0 + -100000 Combine like terms: 0 + -100000 = -100000 -2100x + x2 = -100000 The x term is -2100x. Take half its coefficient (-1050). Square it (1102500) and add it to both sides. Add '1102500' to each side of the equation. -2100x + 1102500 + x2 = -100000 + 1102500 Reorder the terms: 1102500 + -2100x + x2 = -100000 + 1102500 Combine like terms: -100000 + 1102500 = 1002500 1102500 + -2100x + x2 = 1002500 Factor a perfect square on the left side: (x + -1050)(x + -1050) = 1002500 Calculate the square root of the right side: 1001.249219725 Break this problem into two subproblems by setting (x + -1050) equal to 1001.249219725 and -1001.249219725.Subproblem 1
x + -1050 = 1001.249219725 Simplifying x + -1050 = 1001.249219725 Reorder the terms: -1050 + x = 1001.249219725 Solving -1050 + x = 1001.249219725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1050' to each side of the equation. -1050 + 1050 + x = 1001.249219725 + 1050 Combine like terms: -1050 + 1050 = 0 0 + x = 1001.249219725 + 1050 x = 1001.249219725 + 1050 Combine like terms: 1001.249219725 + 1050 = 2051.249219725 x = 2051.249219725 Simplifying x = 2051.249219725Subproblem 2
x + -1050 = -1001.249219725 Simplifying x + -1050 = -1001.249219725 Reorder the terms: -1050 + x = -1001.249219725 Solving -1050 + x = -1001.249219725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1050' to each side of the equation. -1050 + 1050 + x = -1001.249219725 + 1050 Combine like terms: -1050 + 1050 = 0 0 + x = -1001.249219725 + 1050 x = -1001.249219725 + 1050 Combine like terms: -1001.249219725 + 1050 = 48.750780275 x = 48.750780275 Simplifying x = 48.750780275Solution
The solution to the problem is based on the solutions from the subproblems. x = {2051.249219725, 48.750780275}
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