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Simplifying x2 + -1x + -2025 = 0 Reorder the terms: -2025 + -1x + x2 = 0 Solving -2025 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2025' to each side of the equation. -2025 + -1x + 2025 + x2 = 0 + 2025 Reorder the terms: -2025 + 2025 + -1x + x2 = 0 + 2025 Combine like terms: -2025 + 2025 = 0 0 + -1x + x2 = 0 + 2025 -1x + x2 = 0 + 2025 Combine like terms: 0 + 2025 = 2025 -1x + x2 = 2025 The x term is -1x. 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. -1x + 0.25 + x2 = 2025 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 2025 + 0.25 Combine like terms: 2025 + 0.25 = 2025.25 0.25 + -1x + x2 = 2025.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 2025.25 Calculate the square root of the right side: 45.002777692 Break this problem into two subproblems by setting (x + -0.5) equal to 45.002777692 and -45.002777692.Subproblem 1
x + -0.5 = 45.002777692 Simplifying x + -0.5 = 45.002777692 Reorder the terms: -0.5 + x = 45.002777692 Solving -0.5 + x = 45.002777692 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 = 45.002777692 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 45.002777692 + 0.5 x = 45.002777692 + 0.5 Combine like terms: 45.002777692 + 0.5 = 45.502777692 x = 45.502777692 Simplifying x = 45.502777692Subproblem 2
x + -0.5 = -45.002777692 Simplifying x + -0.5 = -45.002777692 Reorder the terms: -0.5 + x = -45.002777692 Solving -0.5 + x = -45.002777692 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 = -45.002777692 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -45.002777692 + 0.5 x = -45.002777692 + 0.5 Combine like terms: -45.002777692 + 0.5 = -44.502777692 x = -44.502777692 Simplifying x = -44.502777692Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.502777692, -44.502777692}
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