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Simplifying x2 + -1x + -3600 = 0 Reorder the terms: -3600 + -1x + x2 = 0 Solving -3600 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3600' to each side of the equation. -3600 + -1x + 3600 + x2 = 0 + 3600 Reorder the terms: -3600 + 3600 + -1x + x2 = 0 + 3600 Combine like terms: -3600 + 3600 = 0 0 + -1x + x2 = 0 + 3600 -1x + x2 = 0 + 3600 Combine like terms: 0 + 3600 = 3600 -1x + x2 = 3600 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 = 3600 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 3600 + 0.25 Combine like terms: 3600 + 0.25 = 3600.25 0.25 + -1x + x2 = 3600.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 3600.25 Calculate the square root of the right side: 60.002083297 Break this problem into two subproblems by setting (x + -0.5) equal to 60.002083297 and -60.002083297.Subproblem 1
x + -0.5 = 60.002083297 Simplifying x + -0.5 = 60.002083297 Reorder the terms: -0.5 + x = 60.002083297 Solving -0.5 + x = 60.002083297 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 = 60.002083297 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 60.002083297 + 0.5 x = 60.002083297 + 0.5 Combine like terms: 60.002083297 + 0.5 = 60.502083297 x = 60.502083297 Simplifying x = 60.502083297Subproblem 2
x + -0.5 = -60.002083297 Simplifying x + -0.5 = -60.002083297 Reorder the terms: -0.5 + x = -60.002083297 Solving -0.5 + x = -60.002083297 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 = -60.002083297 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -60.002083297 + 0.5 x = -60.002083297 + 0.5 Combine like terms: -60.002083297 + 0.5 = -59.502083297 x = -59.502083297 Simplifying x = -59.502083297Solution
The solution to the problem is based on the solutions from the subproblems. x = {60.502083297, -59.502083297}
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