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Simplifying (3812500 + -125000x) * x + -10.29x + -12320000 = 0 Reorder the terms for easier multiplication: x(3812500 + -125000x) + -10.29x + -12320000 = 0 (3812500 * x + -125000x * x) + -10.29x + -12320000 = 0 (3812500x + -125000x2) + -10.29x + -12320000 = 0 Reorder the terms: -12320000 + 3812500x + -10.29x + -125000x2 = 0 Combine like terms: 3812500x + -10.29x = 3812489.71x -12320000 + 3812489.71x + -125000x2 = 0 Solving -12320000 + 3812489.71x + -125000x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -125000 the coefficient of the squared term: Divide each side by '-125000'. 98.56 + -30.49991768x + x2 = 0 Move the constant term to the right: Add '-98.56' to each side of the equation. 98.56 + -30.49991768x + -98.56 + x2 = 0 + -98.56 Reorder the terms: 98.56 + -98.56 + -30.49991768x + x2 = 0 + -98.56 Combine like terms: 98.56 + -98.56 = 0.00 0.00 + -30.49991768x + x2 = 0 + -98.56 -30.49991768x + x2 = 0 + -98.56 Combine like terms: 0 + -98.56 = -98.56 -30.49991768x + x2 = -98.56 The x term is -30.49991768x. Take half its coefficient (-15.24995884). Square it (232.5612446) and add it to both sides. Add '232.5612446' to each side of the equation. -30.49991768x + 232.5612446 + x2 = -98.56 + 232.5612446 Reorder the terms: 232.5612446 + -30.49991768x + x2 = -98.56 + 232.5612446 Combine like terms: -98.56 + 232.5612446 = 134.0012446 232.5612446 + -30.49991768x + x2 = 134.0012446 Factor a perfect square on the left side: (x + -15.24995884)(x + -15.24995884) = 134.0012446 Calculate the square root of the right side: 11.575890661 Break this problem into two subproblems by setting (x + -15.24995884) equal to 11.575890661 and -11.575890661.Subproblem 1
x + -15.24995884 = 11.575890661 Simplifying x + -15.24995884 = 11.575890661 Reorder the terms: -15.24995884 + x = 11.575890661 Solving -15.24995884 + x = 11.575890661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.24995884' to each side of the equation. -15.24995884 + 15.24995884 + x = 11.575890661 + 15.24995884 Combine like terms: -15.24995884 + 15.24995884 = 0.00000000 0.00000000 + x = 11.575890661 + 15.24995884 x = 11.575890661 + 15.24995884 Combine like terms: 11.575890661 + 15.24995884 = 26.825849501 x = 26.825849501 Simplifying x = 26.825849501Subproblem 2
x + -15.24995884 = -11.575890661 Simplifying x + -15.24995884 = -11.575890661 Reorder the terms: -15.24995884 + x = -11.575890661 Solving -15.24995884 + x = -11.575890661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.24995884' to each side of the equation. -15.24995884 + 15.24995884 + x = -11.575890661 + 15.24995884 Combine like terms: -15.24995884 + 15.24995884 = 0.00000000 0.00000000 + x = -11.575890661 + 15.24995884 x = -11.575890661 + 15.24995884 Combine like terms: -11.575890661 + 15.24995884 = 3.674068179 x = 3.674068179 Simplifying x = 3.674068179Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.825849501, 3.674068179}
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