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Simplifying x2 + -1793x + 4200 = 0 Reorder the terms: 4200 + -1793x + x2 = 0 Solving 4200 + -1793x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-4200' to each side of the equation. 4200 + -1793x + -4200 + x2 = 0 + -4200 Reorder the terms: 4200 + -4200 + -1793x + x2 = 0 + -4200 Combine like terms: 4200 + -4200 = 0 0 + -1793x + x2 = 0 + -4200 -1793x + x2 = 0 + -4200 Combine like terms: 0 + -4200 = -4200 -1793x + x2 = -4200 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 = -4200 + 803712.25 Reorder the terms: 803712.25 + -1793x + x2 = -4200 + 803712.25 Combine like terms: -4200 + 803712.25 = 799512.25 803712.25 + -1793x + x2 = 799512.25 Factor a perfect square on the left side: (x + -896.5)(x + -896.5) = 799512.25 Calculate the square root of the right side: 894.154488889 Break this problem into two subproblems by setting (x + -896.5) equal to 894.154488889 and -894.154488889.Subproblem 1
x + -896.5 = 894.154488889 Simplifying x + -896.5 = 894.154488889 Reorder the terms: -896.5 + x = 894.154488889 Solving -896.5 + x = 894.154488889 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 = 894.154488889 + 896.5 Combine like terms: -896.5 + 896.5 = 0.0 0.0 + x = 894.154488889 + 896.5 x = 894.154488889 + 896.5 Combine like terms: 894.154488889 + 896.5 = 1790.654488889 x = 1790.654488889 Simplifying x = 1790.654488889Subproblem 2
x + -896.5 = -894.154488889 Simplifying x + -896.5 = -894.154488889 Reorder the terms: -896.5 + x = -894.154488889 Solving -896.5 + x = -894.154488889 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 = -894.154488889 + 896.5 Combine like terms: -896.5 + 896.5 = 0.0 0.0 + x = -894.154488889 + 896.5 x = -894.154488889 + 896.5 Combine like terms: -894.154488889 + 896.5 = 2.345511111 x = 2.345511111 Simplifying x = 2.345511111Solution
The solution to the problem is based on the solutions from the subproblems. x = {1790.654488889, 2.345511111}
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