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Simplifying x2 + x = 3600000000 Reorder the terms: x + x2 = 3600000000 Solving x + x2 = 3600000000 Solving for variable 'x'. Reorder the terms: -3600000000 + x + x2 = 3600000000 + -3600000000 Combine like terms: 3600000000 + -3600000000 = 0 -3600000000 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3600000000' to each side of the equation. -3600000000 + x + 3600000000 + x2 = 0 + 3600000000 Reorder the terms: -3600000000 + 3600000000 + x + x2 = 0 + 3600000000 Combine like terms: -3600000000 + 3600000000 = 0 0 + x + x2 = 0 + 3600000000 x + x2 = 0 + 3600000000 Combine like terms: 0 + 3600000000 = 3600000000 x + x2 = 3600000000 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 = 3600000000 + 0.25 Reorder the terms: 0.25 + x + x2 = 3600000000 + 0.25 Combine like terms: 3600000000 + 0.25 = 3600000000.25 0.25 + x + x2 = 3600000000.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3600000000.25 Calculate the square root of the right side: 60000.000002083 Break this problem into two subproblems by setting (x + 0.5) equal to 60000.000002083 and -60000.000002083.Subproblem 1
x + 0.5 = 60000.000002083 Simplifying x + 0.5 = 60000.000002083 Reorder the terms: 0.5 + x = 60000.000002083 Solving 0.5 + x = 60000.000002083 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 = 60000.000002083 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 60000.000002083 + -0.5 x = 60000.000002083 + -0.5 Combine like terms: 60000.000002083 + -0.5 = 59999.500002083 x = 59999.500002083 Simplifying x = 59999.500002083Subproblem 2
x + 0.5 = -60000.000002083 Simplifying x + 0.5 = -60000.000002083 Reorder the terms: 0.5 + x = -60000.000002083 Solving 0.5 + x = -60000.000002083 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 = -60000.000002083 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -60000.000002083 + -0.5 x = -60000.000002083 + -0.5 Combine like terms: -60000.000002083 + -0.5 = -60000.500002083 x = -60000.500002083 Simplifying x = -60000.500002083Solution
The solution to the problem is based on the solutions from the subproblems. x = {59999.500002083, -60000.500002083}
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