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Simplifying x(1801 + -1x) = 2700 (1801 * x + -1x * x) = 2700 (1801x + -1x2) = 2700 Solving 1801x + -1x2 = 2700 Solving for variable 'x'. Reorder the terms: -2700 + 1801x + -1x2 = 2700 + -2700 Combine like terms: 2700 + -2700 = 0 -2700 + 1801x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2700 + -1801x + x2 = 0 Move the constant term to the right: Add '-2700' to each side of the equation. 2700 + -1801x + -2700 + x2 = 0 + -2700 Reorder the terms: 2700 + -2700 + -1801x + x2 = 0 + -2700 Combine like terms: 2700 + -2700 = 0 0 + -1801x + x2 = 0 + -2700 -1801x + x2 = 0 + -2700 Combine like terms: 0 + -2700 = -2700 -1801x + x2 = -2700 The x term is -1801x. Take half its coefficient (-900.5). Square it (810900.25) and add it to both sides. Add '810900.25' to each side of the equation. -1801x + 810900.25 + x2 = -2700 + 810900.25 Reorder the terms: 810900.25 + -1801x + x2 = -2700 + 810900.25 Combine like terms: -2700 + 810900.25 = 808200.25 810900.25 + -1801x + x2 = 808200.25 Factor a perfect square on the left side: (x + -900.5)(x + -900.5) = 808200.25 Calculate the square root of the right side: 898.99958287 Break this problem into two subproblems by setting (x + -900.5) equal to 898.99958287 and -898.99958287.Subproblem 1
x + -900.5 = 898.99958287 Simplifying x + -900.5 = 898.99958287 Reorder the terms: -900.5 + x = 898.99958287 Solving -900.5 + x = 898.99958287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '900.5' to each side of the equation. -900.5 + 900.5 + x = 898.99958287 + 900.5 Combine like terms: -900.5 + 900.5 = 0.0 0.0 + x = 898.99958287 + 900.5 x = 898.99958287 + 900.5 Combine like terms: 898.99958287 + 900.5 = 1799.49958287 x = 1799.49958287 Simplifying x = 1799.49958287Subproblem 2
x + -900.5 = -898.99958287 Simplifying x + -900.5 = -898.99958287 Reorder the terms: -900.5 + x = -898.99958287 Solving -900.5 + x = -898.99958287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '900.5' to each side of the equation. -900.5 + 900.5 + x = -898.99958287 + 900.5 Combine like terms: -900.5 + 900.5 = 0.0 0.0 + x = -898.99958287 + 900.5 x = -898.99958287 + 900.5 Combine like terms: -898.99958287 + 900.5 = 1.50041713 x = 1.50041713 Simplifying x = 1.50041713Solution
The solution to the problem is based on the solutions from the subproblems. x = {1799.49958287, 1.50041713}
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