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Simplifying x2 + -140.5x + 2467.812258 = 0 Reorder the terms: 2467.812258 + -140.5x + x2 = 0 Solving 2467.812258 + -140.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2467.812258' to each side of the equation. 2467.812258 + -140.5x + -2467.812258 + x2 = 0 + -2467.812258 Reorder the terms: 2467.812258 + -2467.812258 + -140.5x + x2 = 0 + -2467.812258 Combine like terms: 2467.812258 + -2467.812258 = 0.000000 0.000000 + -140.5x + x2 = 0 + -2467.812258 -140.5x + x2 = 0 + -2467.812258 Combine like terms: 0 + -2467.812258 = -2467.812258 -140.5x + x2 = -2467.812258 The x term is -140.5x. Take half its coefficient (-70.25). Square it (4935.0625) and add it to both sides. Add '4935.0625' to each side of the equation. -140.5x + 4935.0625 + x2 = -2467.812258 + 4935.0625 Reorder the terms: 4935.0625 + -140.5x + x2 = -2467.812258 + 4935.0625 Combine like terms: -2467.812258 + 4935.0625 = 2467.250242 4935.0625 + -140.5x + x2 = 2467.250242 Factor a perfect square on the left side: (x + -70.25)(x + -70.25) = 2467.250242 Calculate the square root of the right side: 49.67142279 Break this problem into two subproblems by setting (x + -70.25) equal to 49.67142279 and -49.67142279.Subproblem 1
x + -70.25 = 49.67142279 Simplifying x + -70.25 = 49.67142279 Reorder the terms: -70.25 + x = 49.67142279 Solving -70.25 + x = 49.67142279 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '70.25' to each side of the equation. -70.25 + 70.25 + x = 49.67142279 + 70.25 Combine like terms: -70.25 + 70.25 = 0.00 0.00 + x = 49.67142279 + 70.25 x = 49.67142279 + 70.25 Combine like terms: 49.67142279 + 70.25 = 119.92142279 x = 119.92142279 Simplifying x = 119.92142279Subproblem 2
x + -70.25 = -49.67142279 Simplifying x + -70.25 = -49.67142279 Reorder the terms: -70.25 + x = -49.67142279 Solving -70.25 + x = -49.67142279 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '70.25' to each side of the equation. -70.25 + 70.25 + x = -49.67142279 + 70.25 Combine like terms: -70.25 + 70.25 = 0.00 0.00 + x = -49.67142279 + 70.25 x = -49.67142279 + 70.25 Combine like terms: -49.67142279 + 70.25 = 20.57857721 x = 20.57857721 Simplifying x = 20.57857721Solution
The solution to the problem is based on the solutions from the subproblems. x = {119.92142279, 20.57857721}
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