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Simplifying x2 + x = 270000 Reorder the terms: x + x2 = 270000 Solving x + x2 = 270000 Solving for variable 'x'. Reorder the terms: -270000 + x + x2 = 270000 + -270000 Combine like terms: 270000 + -270000 = 0 -270000 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '270000' to each side of the equation. -270000 + x + 270000 + x2 = 0 + 270000 Reorder the terms: -270000 + 270000 + x + x2 = 0 + 270000 Combine like terms: -270000 + 270000 = 0 0 + x + x2 = 0 + 270000 x + x2 = 0 + 270000 Combine like terms: 0 + 270000 = 270000 x + x2 = 270000 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 270000 + 0.25 Reorder the terms: 0.25 + x + x2 = 270000 + 0.25 Combine like terms: 270000 + 0.25 = 270000.25 0.25 + x + x2 = 270000.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 270000.25 Calculate the square root of the right side: 519.615482833 Break this problem into two subproblems by setting (x + 0.5) equal to 519.615482833 and -519.615482833.Subproblem 1
x + 0.5 = 519.615482833 Simplifying x + 0.5 = 519.615482833 Reorder the terms: 0.5 + x = 519.615482833 Solving 0.5 + x = 519.615482833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 519.615482833 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 519.615482833 + -0.5 x = 519.615482833 + -0.5 Combine like terms: 519.615482833 + -0.5 = 519.115482833 x = 519.115482833 Simplifying x = 519.115482833Subproblem 2
x + 0.5 = -519.615482833 Simplifying x + 0.5 = -519.615482833 Reorder the terms: 0.5 + x = -519.615482833 Solving 0.5 + x = -519.615482833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -519.615482833 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -519.615482833 + -0.5 x = -519.615482833 + -0.5 Combine like terms: -519.615482833 + -0.5 = -520.115482833 x = -520.115482833 Simplifying x = -520.115482833Solution
The solution to the problem is based on the solutions from the subproblems. x = {519.115482833, -520.115482833}
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