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Simplifying x2 + -99x + -2 = 0 Reorder the terms: -2 + -99x + x2 = 0 Solving -2 + -99x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -99x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -99x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -99x + x2 = 0 + 2 -99x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -99x + x2 = 2 The x term is -99x. Take half its coefficient (-49.5). Square it (2450.25) and add it to both sides. Add '2450.25' to each side of the equation. -99x + 2450.25 + x2 = 2 + 2450.25 Reorder the terms: 2450.25 + -99x + x2 = 2 + 2450.25 Combine like terms: 2 + 2450.25 = 2452.25 2450.25 + -99x + x2 = 2452.25 Factor a perfect square on the left side: (x + -49.5)(x + -49.5) = 2452.25 Calculate the square root of the right side: 49.520197899 Break this problem into two subproblems by setting (x + -49.5) equal to 49.520197899 and -49.520197899.Subproblem 1
x + -49.5 = 49.520197899 Simplifying x + -49.5 = 49.520197899 Reorder the terms: -49.5 + x = 49.520197899 Solving -49.5 + x = 49.520197899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '49.5' to each side of the equation. -49.5 + 49.5 + x = 49.520197899 + 49.5 Combine like terms: -49.5 + 49.5 = 0.0 0.0 + x = 49.520197899 + 49.5 x = 49.520197899 + 49.5 Combine like terms: 49.520197899 + 49.5 = 99.020197899 x = 99.020197899 Simplifying x = 99.020197899Subproblem 2
x + -49.5 = -49.520197899 Simplifying x + -49.5 = -49.520197899 Reorder the terms: -49.5 + x = -49.520197899 Solving -49.5 + x = -49.520197899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '49.5' to each side of the equation. -49.5 + 49.5 + x = -49.520197899 + 49.5 Combine like terms: -49.5 + 49.5 = 0.0 0.0 + x = -49.520197899 + 49.5 x = -49.520197899 + 49.5 Combine like terms: -49.520197899 + 49.5 = -0.020197899 x = -0.020197899 Simplifying x = -0.020197899Solution
The solution to the problem is based on the solutions from the subproblems. x = {99.020197899, -0.020197899}
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