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Simplifying X2 + -2000X + 555556 = 0 Reorder the terms: 555556 + -2000X + X2 = 0 Solving 555556 + -2000X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '-555556' to each side of the equation. 555556 + -2000X + -555556 + X2 = 0 + -555556 Reorder the terms: 555556 + -555556 + -2000X + X2 = 0 + -555556 Combine like terms: 555556 + -555556 = 0 0 + -2000X + X2 = 0 + -555556 -2000X + X2 = 0 + -555556 Combine like terms: 0 + -555556 = -555556 -2000X + X2 = -555556 The X term is -2000X. Take half its coefficient (-1000). Square it (1000000) and add it to both sides. Add '1000000' to each side of the equation. -2000X + 1000000 + X2 = -555556 + 1000000 Reorder the terms: 1000000 + -2000X + X2 = -555556 + 1000000 Combine like terms: -555556 + 1000000 = 444444 1000000 + -2000X + X2 = 444444 Factor a perfect square on the left side: (X + -1000)(X + -1000) = 444444 Calculate the square root of the right side: 666.666333333 Break this problem into two subproblems by setting (X + -1000) equal to 666.666333333 and -666.666333333.Subproblem 1
X + -1000 = 666.666333333 Simplifying X + -1000 = 666.666333333 Reorder the terms: -1000 + X = 666.666333333 Solving -1000 + X = 666.666333333 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1000' to each side of the equation. -1000 + 1000 + X = 666.666333333 + 1000 Combine like terms: -1000 + 1000 = 0 0 + X = 666.666333333 + 1000 X = 666.666333333 + 1000 Combine like terms: 666.666333333 + 1000 = 1666.666333333 X = 1666.666333333 Simplifying X = 1666.666333333Subproblem 2
X + -1000 = -666.666333333 Simplifying X + -1000 = -666.666333333 Reorder the terms: -1000 + X = -666.666333333 Solving -1000 + X = -666.666333333 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1000' to each side of the equation. -1000 + 1000 + X = -666.666333333 + 1000 Combine like terms: -1000 + 1000 = 0 0 + X = -666.666333333 + 1000 X = -666.666333333 + 1000 Combine like terms: -666.666333333 + 1000 = 333.333666667 X = 333.333666667 Simplifying X = 333.333666667Solution
The solution to the problem is based on the solutions from the subproblems. X = {1666.666333333, 333.333666667}
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