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Simplifying x2 + 93x + 285 = 0 Reorder the terms: 285 + 93x + x2 = 0 Solving 285 + 93x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-285' to each side of the equation. 285 + 93x + -285 + x2 = 0 + -285 Reorder the terms: 285 + -285 + 93x + x2 = 0 + -285 Combine like terms: 285 + -285 = 0 0 + 93x + x2 = 0 + -285 93x + x2 = 0 + -285 Combine like terms: 0 + -285 = -285 93x + x2 = -285 The x term is 93x. Take half its coefficient (46.5). Square it (2162.25) and add it to both sides. Add '2162.25' to each side of the equation. 93x + 2162.25 + x2 = -285 + 2162.25 Reorder the terms: 2162.25 + 93x + x2 = -285 + 2162.25 Combine like terms: -285 + 2162.25 = 1877.25 2162.25 + 93x + x2 = 1877.25 Factor a perfect square on the left side: (x + 46.5)(x + 46.5) = 1877.25 Calculate the square root of the right side: 43.327243162 Break this problem into two subproblems by setting (x + 46.5) equal to 43.327243162 and -43.327243162.Subproblem 1
x + 46.5 = 43.327243162 Simplifying x + 46.5 = 43.327243162 Reorder the terms: 46.5 + x = 43.327243162 Solving 46.5 + x = 43.327243162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-46.5' to each side of the equation. 46.5 + -46.5 + x = 43.327243162 + -46.5 Combine like terms: 46.5 + -46.5 = 0.0 0.0 + x = 43.327243162 + -46.5 x = 43.327243162 + -46.5 Combine like terms: 43.327243162 + -46.5 = -3.172756838 x = -3.172756838 Simplifying x = -3.172756838Subproblem 2
x + 46.5 = -43.327243162 Simplifying x + 46.5 = -43.327243162 Reorder the terms: 46.5 + x = -43.327243162 Solving 46.5 + x = -43.327243162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-46.5' to each side of the equation. 46.5 + -46.5 + x = -43.327243162 + -46.5 Combine like terms: 46.5 + -46.5 = 0.0 0.0 + x = -43.327243162 + -46.5 x = -43.327243162 + -46.5 Combine like terms: -43.327243162 + -46.5 = -89.827243162 x = -89.827243162 Simplifying x = -89.827243162Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.172756838, -89.827243162}
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