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Simplifying 2x2 + -268x + -5645 = 0 Reorder the terms: -5645 + -268x + 2x2 = 0 Solving -5645 + -268x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2822.5 + -134x + x2 = 0 Move the constant term to the right: Add '2822.5' to each side of the equation. -2822.5 + -134x + 2822.5 + x2 = 0 + 2822.5 Reorder the terms: -2822.5 + 2822.5 + -134x + x2 = 0 + 2822.5 Combine like terms: -2822.5 + 2822.5 = 0.0 0.0 + -134x + x2 = 0 + 2822.5 -134x + x2 = 0 + 2822.5 Combine like terms: 0 + 2822.5 = 2822.5 -134x + x2 = 2822.5 The x term is -134x. Take half its coefficient (-67). Square it (4489) and add it to both sides. Add '4489' to each side of the equation. -134x + 4489 + x2 = 2822.5 + 4489 Reorder the terms: 4489 + -134x + x2 = 2822.5 + 4489 Combine like terms: 2822.5 + 4489 = 7311.5 4489 + -134x + x2 = 7311.5 Factor a perfect square on the left side: (x + -67)(x + -67) = 7311.5 Calculate the square root of the right side: 85.507309629 Break this problem into two subproblems by setting (x + -67) equal to 85.507309629 and -85.507309629.Subproblem 1
x + -67 = 85.507309629 Simplifying x + -67 = 85.507309629 Reorder the terms: -67 + x = 85.507309629 Solving -67 + x = 85.507309629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '67' to each side of the equation. -67 + 67 + x = 85.507309629 + 67 Combine like terms: -67 + 67 = 0 0 + x = 85.507309629 + 67 x = 85.507309629 + 67 Combine like terms: 85.507309629 + 67 = 152.507309629 x = 152.507309629 Simplifying x = 152.507309629Subproblem 2
x + -67 = -85.507309629 Simplifying x + -67 = -85.507309629 Reorder the terms: -67 + x = -85.507309629 Solving -67 + x = -85.507309629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '67' to each side of the equation. -67 + 67 + x = -85.507309629 + 67 Combine like terms: -67 + 67 = 0 0 + x = -85.507309629 + 67 x = -85.507309629 + 67 Combine like terms: -85.507309629 + 67 = -18.507309629 x = -18.507309629 Simplifying x = -18.507309629Solution
The solution to the problem is based on the solutions from the subproblems. x = {152.507309629, -18.507309629}
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