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Simplifying 4480 = x(82000 + -1x) 4480 = (82000 * x + -1x * x) 4480 = (82000x + -1x2) Solving 4480 = 82000x + -1x2 Solving for variable 'x'. Reorder the terms: 4480 + -82000x + x2 = 82000x + -82000x + -1x2 + x2 Combine like terms: 82000x + -82000x = 0 4480 + -82000x + x2 = 0 + -1x2 + x2 4480 + -82000x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 4480 + -82000x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4480' to each side of the equation. 4480 + -82000x + -4480 + x2 = 0 + -4480 Reorder the terms: 4480 + -4480 + -82000x + x2 = 0 + -4480 Combine like terms: 4480 + -4480 = 0 0 + -82000x + x2 = 0 + -4480 -82000x + x2 = 0 + -4480 Combine like terms: 0 + -4480 = -4480 -82000x + x2 = -4480 The x term is -82000x. Take half its coefficient (-41000). Square it (1681000000) and add it to both sides. Add '1681000000' to each side of the equation. -82000x + 1681000000 + x2 = -4480 + 1681000000 Reorder the terms: 1681000000 + -82000x + x2 = -4480 + 1681000000 Combine like terms: -4480 + 1681000000 = 1680995520 1681000000 + -82000x + x2 = 1680995520 Factor a perfect square on the left side: (x + -41000)(x + -41000) = 1680995520 Calculate the square root of the right side: 40999.945365817 Break this problem into two subproblems by setting (x + -41000) equal to 40999.945365817 and -40999.945365817.Subproblem 1
x + -41000 = 40999.945365817 Simplifying x + -41000 = 40999.945365817 Reorder the terms: -41000 + x = 40999.945365817 Solving -41000 + x = 40999.945365817 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '41000' to each side of the equation. -41000 + 41000 + x = 40999.945365817 + 41000 Combine like terms: -41000 + 41000 = 0 0 + x = 40999.945365817 + 41000 x = 40999.945365817 + 41000 Combine like terms: 40999.945365817 + 41000 = 81999.945365817 x = 81999.945365817 Simplifying x = 81999.945365817Subproblem 2
x + -41000 = -40999.945365817 Simplifying x + -41000 = -40999.945365817 Reorder the terms: -41000 + x = -40999.945365817 Solving -41000 + x = -40999.945365817 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '41000' to each side of the equation. -41000 + 41000 + x = -40999.945365817 + 41000 Combine like terms: -41000 + 41000 = 0 0 + x = -40999.945365817 + 41000 x = -40999.945365817 + 41000 Combine like terms: -40999.945365817 + 41000 = 0.054634183 x = 0.054634183 Simplifying x = 0.054634183Solution
The solution to the problem is based on the solutions from the subproblems. x = {81999.945365817, 0.054634183}
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