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Simplifying x2 + -1793x + 16800 = 0 Reorder the terms: 16800 + -1793x + x2 = 0 Solving 16800 + -1793x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-16800' to each side of the equation. 16800 + -1793x + -16800 + x2 = 0 + -16800 Reorder the terms: 16800 + -16800 + -1793x + x2 = 0 + -16800 Combine like terms: 16800 + -16800 = 0 0 + -1793x + x2 = 0 + -16800 -1793x + x2 = 0 + -16800 Combine like terms: 0 + -16800 = -16800 -1793x + x2 = -16800 The x term is -1793x. Take half its coefficient (-896.5). Square it (803712.25) and add it to both sides. Add '803712.25' to each side of the equation. -1793x + 803712.25 + x2 = -16800 + 803712.25 Reorder the terms: 803712.25 + -1793x + x2 = -16800 + 803712.25 Combine like terms: -16800 + 803712.25 = 786912.25 803712.25 + -1793x + x2 = 786912.25 Factor a perfect square on the left side: (x + -896.5)(x + -896.5) = 786912.25 Calculate the square root of the right side: 887.080746043 Break this problem into two subproblems by setting (x + -896.5) equal to 887.080746043 and -887.080746043.Subproblem 1
x + -896.5 = 887.080746043 Simplifying x + -896.5 = 887.080746043 Reorder the terms: -896.5 + x = 887.080746043 Solving -896.5 + x = 887.080746043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '896.5' to each side of the equation. -896.5 + 896.5 + x = 887.080746043 + 896.5 Combine like terms: -896.5 + 896.5 = 0.0 0.0 + x = 887.080746043 + 896.5 x = 887.080746043 + 896.5 Combine like terms: 887.080746043 + 896.5 = 1783.580746043 x = 1783.580746043 Simplifying x = 1783.580746043Subproblem 2
x + -896.5 = -887.080746043 Simplifying x + -896.5 = -887.080746043 Reorder the terms: -896.5 + x = -887.080746043 Solving -896.5 + x = -887.080746043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '896.5' to each side of the equation. -896.5 + 896.5 + x = -887.080746043 + 896.5 Combine like terms: -896.5 + 896.5 = 0.0 0.0 + x = -887.080746043 + 896.5 x = -887.080746043 + 896.5 Combine like terms: -887.080746043 + 896.5 = 9.419253957 x = 9.419253957 Simplifying x = 9.419253957Solution
The solution to the problem is based on the solutions from the subproblems. x = {1783.580746043, 9.419253957}
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