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Simplifying (x2) + x = 660000 x2 + x = 660000 Reorder the terms: x + x2 = 660000 Solving x + x2 = 660000 Solving for variable 'x'. Reorder the terms: -660000 + x + x2 = 660000 + -660000 Combine like terms: 660000 + -660000 = 0 -660000 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '660000' to each side of the equation. -660000 + x + 660000 + x2 = 0 + 660000 Reorder the terms: -660000 + 660000 + x + x2 = 0 + 660000 Combine like terms: -660000 + 660000 = 0 0 + x + x2 = 0 + 660000 x + x2 = 0 + 660000 Combine like terms: 0 + 660000 = 660000 x + x2 = 660000 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 = 660000 + 0.25 Reorder the terms: 0.25 + x + x2 = 660000 + 0.25 Combine like terms: 660000 + 0.25 = 660000.25 0.25 + x + x2 = 660000.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 660000.25 Calculate the square root of the right side: 812.403994328 Break this problem into two subproblems by setting (x + 0.5) equal to 812.403994328 and -812.403994328.Subproblem 1
x + 0.5 = 812.403994328 Simplifying x + 0.5 = 812.403994328 Reorder the terms: 0.5 + x = 812.403994328 Solving 0.5 + x = 812.403994328 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 = 812.403994328 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 812.403994328 + -0.5 x = 812.403994328 + -0.5 Combine like terms: 812.403994328 + -0.5 = 811.903994328 x = 811.903994328 Simplifying x = 811.903994328Subproblem 2
x + 0.5 = -812.403994328 Simplifying x + 0.5 = -812.403994328 Reorder the terms: 0.5 + x = -812.403994328 Solving 0.5 + x = -812.403994328 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 = -812.403994328 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -812.403994328 + -0.5 x = -812.403994328 + -0.5 Combine like terms: -812.403994328 + -0.5 = -812.903994328 x = -812.903994328 Simplifying x = -812.903994328Solution
The solution to the problem is based on the solutions from the subproblems. x = {811.903994328, -812.903994328}
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