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Simplifying x2 + -118674x + 1169640 = 0 Reorder the terms: 1169640 + -118674x + x2 = 0 Solving 1169640 + -118674x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1169640' to each side of the equation. 1169640 + -118674x + -1169640 + x2 = 0 + -1169640 Reorder the terms: 1169640 + -1169640 + -118674x + x2 = 0 + -1169640 Combine like terms: 1169640 + -1169640 = 0 0 + -118674x + x2 = 0 + -1169640 -118674x + x2 = 0 + -1169640 Combine like terms: 0 + -1169640 = -1169640 -118674x + x2 = -1169640 The x term is -118674x. Take half its coefficient (-59337). Square it (3520879569) and add it to both sides. Add '3520879569' to each side of the equation. -118674x + 3520879569 + x2 = -1169640 + 3520879569 Reorder the terms: 3520879569 + -118674x + x2 = -1169640 + 3520879569 Combine like terms: -1169640 + 3520879569 = 3519709929 3520879569 + -118674x + x2 = 3519709929 Factor a perfect square on the left side: (x + -59337)(x + -59337) = 3519709929 Calculate the square root of the right side: 59327.143273547 Break this problem into two subproblems by setting (x + -59337) equal to 59327.143273547 and -59327.143273547.Subproblem 1
x + -59337 = 59327.143273547 Simplifying x + -59337 = 59327.143273547 Reorder the terms: -59337 + x = 59327.143273547 Solving -59337 + x = 59327.143273547 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '59337' to each side of the equation. -59337 + 59337 + x = 59327.143273547 + 59337 Combine like terms: -59337 + 59337 = 0 0 + x = 59327.143273547 + 59337 x = 59327.143273547 + 59337 Combine like terms: 59327.143273547 + 59337 = 118664.143273547 x = 118664.143273547 Simplifying x = 118664.143273547Subproblem 2
x + -59337 = -59327.143273547 Simplifying x + -59337 = -59327.143273547 Reorder the terms: -59337 + x = -59327.143273547 Solving -59337 + x = -59327.143273547 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '59337' to each side of the equation. -59337 + 59337 + x = -59327.143273547 + 59337 Combine like terms: -59337 + 59337 = 0 0 + x = -59327.143273547 + 59337 x = -59327.143273547 + 59337 Combine like terms: -59327.143273547 + 59337 = 9.856726453 x = 9.856726453 Simplifying x = 9.856726453Solution
The solution to the problem is based on the solutions from the subproblems. x = {118664.143273547, 9.856726453}
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