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Simplifying 2x2 + 85x + -2000 = 0 Reorder the terms: -2000 + 85x + 2x2 = 0 Solving -2000 + 85x + 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'. -1000 + 42.5x + x2 = 0 Move the constant term to the right: Add '1000' to each side of the equation. -1000 + 42.5x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + 42.5x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + 42.5x + x2 = 0 + 1000 42.5x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 42.5x + x2 = 1000 The x term is 42.5x. Take half its coefficient (21.25). Square it (451.5625) and add it to both sides. Add '451.5625' to each side of the equation. 42.5x + 451.5625 + x2 = 1000 + 451.5625 Reorder the terms: 451.5625 + 42.5x + x2 = 1000 + 451.5625 Combine like terms: 1000 + 451.5625 = 1451.5625 451.5625 + 42.5x + x2 = 1451.5625 Factor a perfect square on the left side: (x + 21.25)(x + 21.25) = 1451.5625 Calculate the square root of the right side: 38.099376635 Break this problem into two subproblems by setting (x + 21.25) equal to 38.099376635 and -38.099376635.Subproblem 1
x + 21.25 = 38.099376635 Simplifying x + 21.25 = 38.099376635 Reorder the terms: 21.25 + x = 38.099376635 Solving 21.25 + x = 38.099376635 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21.25' to each side of the equation. 21.25 + -21.25 + x = 38.099376635 + -21.25 Combine like terms: 21.25 + -21.25 = 0.00 0.00 + x = 38.099376635 + -21.25 x = 38.099376635 + -21.25 Combine like terms: 38.099376635 + -21.25 = 16.849376635 x = 16.849376635 Simplifying x = 16.849376635Subproblem 2
x + 21.25 = -38.099376635 Simplifying x + 21.25 = -38.099376635 Reorder the terms: 21.25 + x = -38.099376635 Solving 21.25 + x = -38.099376635 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21.25' to each side of the equation. 21.25 + -21.25 + x = -38.099376635 + -21.25 Combine like terms: 21.25 + -21.25 = 0.00 0.00 + x = -38.099376635 + -21.25 x = -38.099376635 + -21.25 Combine like terms: -38.099376635 + -21.25 = -59.349376635 x = -59.349376635 Simplifying x = -59.349376635Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.849376635, -59.349376635}
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