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Simplifying x2 + -5x + 6 = 2000000 Reorder the terms: 6 + -5x + x2 = 2000000 Solving 6 + -5x + x2 = 2000000 Solving for variable 'x'. Reorder the terms: 6 + -2000000 + -5x + x2 = 2000000 + -2000000 Combine like terms: 6 + -2000000 = -1999994 -1999994 + -5x + x2 = 2000000 + -2000000 Combine like terms: 2000000 + -2000000 = 0 -1999994 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1999994' to each side of the equation. -1999994 + -5x + 1999994 + x2 = 0 + 1999994 Reorder the terms: -1999994 + 1999994 + -5x + x2 = 0 + 1999994 Combine like terms: -1999994 + 1999994 = 0 0 + -5x + x2 = 0 + 1999994 -5x + x2 = 0 + 1999994 Combine like terms: 0 + 1999994 = 1999994 -5x + x2 = 1999994 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 1999994 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 1999994 + 6.25 Combine like terms: 1999994 + 6.25 = 2000000.25 6.25 + -5x + x2 = 2000000.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 2000000.25 Calculate the square root of the right side: 1414.213650761 Break this problem into two subproblems by setting (x + -2.5) equal to 1414.213650761 and -1414.213650761.Subproblem 1
x + -2.5 = 1414.213650761 Simplifying x + -2.5 = 1414.213650761 Reorder the terms: -2.5 + x = 1414.213650761 Solving -2.5 + x = 1414.213650761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 1414.213650761 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1414.213650761 + 2.5 x = 1414.213650761 + 2.5 Combine like terms: 1414.213650761 + 2.5 = 1416.713650761 x = 1416.713650761 Simplifying x = 1416.713650761Subproblem 2
x + -2.5 = -1414.213650761 Simplifying x + -2.5 = -1414.213650761 Reorder the terms: -2.5 + x = -1414.213650761 Solving -2.5 + x = -1414.213650761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -1414.213650761 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1414.213650761 + 2.5 x = -1414.213650761 + 2.5 Combine like terms: -1414.213650761 + 2.5 = -1411.713650761 x = -1411.713650761 Simplifying x = -1411.713650761Solution
The solution to the problem is based on the solutions from the subproblems. x = {1416.713650761, -1411.713650761}
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