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Simplifying x2 + -45x + -2025 = 0 Reorder the terms: -2025 + -45x + x2 = 0 Solving -2025 + -45x + 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 + -45x + 2025 + x2 = 0 + 2025 Reorder the terms: -2025 + 2025 + -45x + x2 = 0 + 2025 Combine like terms: -2025 + 2025 = 0 0 + -45x + x2 = 0 + 2025 -45x + x2 = 0 + 2025 Combine like terms: 0 + 2025 = 2025 -45x + x2 = 2025 The x term is -45x. Take half its coefficient (-22.5). Square it (506.25) and add it to both sides. Add '506.25' to each side of the equation. -45x + 506.25 + x2 = 2025 + 506.25 Reorder the terms: 506.25 + -45x + x2 = 2025 + 506.25 Combine like terms: 2025 + 506.25 = 2531.25 506.25 + -45x + x2 = 2531.25 Factor a perfect square on the left side: (x + -22.5)(x + -22.5) = 2531.25 Calculate the square root of the right side: 50.311529494 Break this problem into two subproblems by setting (x + -22.5) equal to 50.311529494 and -50.311529494.Subproblem 1
x + -22.5 = 50.311529494 Simplifying x + -22.5 = 50.311529494 Reorder the terms: -22.5 + x = 50.311529494 Solving -22.5 + x = 50.311529494 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + x = 50.311529494 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = 50.311529494 + 22.5 x = 50.311529494 + 22.5 Combine like terms: 50.311529494 + 22.5 = 72.811529494 x = 72.811529494 Simplifying x = 72.811529494Subproblem 2
x + -22.5 = -50.311529494 Simplifying x + -22.5 = -50.311529494 Reorder the terms: -22.5 + x = -50.311529494 Solving -22.5 + x = -50.311529494 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + x = -50.311529494 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = -50.311529494 + 22.5 x = -50.311529494 + 22.5 Combine like terms: -50.311529494 + 22.5 = -27.811529494 x = -27.811529494 Simplifying x = -27.811529494Solution
The solution to the problem is based on the solutions from the subproblems. x = {72.811529494, -27.811529494}
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