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Simplifying 209960.735x2 + 31569266222.9275x + -30268631606950 = 0 Reorder the terms: -30268631606950 + 31569266222.9275x + 209960.735x2 = 0 Solving -30268631606950 + 31569266222.9275x + 209960.735x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 209960.735 the coefficient of the squared term: Divide each side by '209960.735'. -144163296.1 + 150357.9525x + x2 = 0 Move the constant term to the right: Add '144163296.1' to each side of the equation. -144163296.1 + 150357.9525x + 144163296.1 + x2 = 0 + 144163296.1 Reorder the terms: -144163296.1 + 144163296.1 + 150357.9525x + x2 = 0 + 144163296.1 Combine like terms: -144163296.1 + 144163296.1 = 0.0 0.0 + 150357.9525x + x2 = 0 + 144163296.1 150357.9525x + x2 = 0 + 144163296.1 Combine like terms: 0 + 144163296.1 = 144163296.1 150357.9525x + x2 = 144163296.1 The x term is 150357.9525x. Take half its coefficient (75178.97625). Square it (5651878470) and add it to both sides. Add '5651878470' to each side of the equation. 150357.9525x + 5651878470 + x2 = 144163296.1 + 5651878470 Reorder the terms: 5651878470 + 150357.9525x + x2 = 144163296.1 + 5651878470 Combine like terms: 144163296.1 + 5651878470 = 5796041766.1 5651878470 + 150357.9525x + x2 = 5796041766.1 Factor a perfect square on the left side: (x + 75178.97625)(x + 75178.97625) = 5796041766.1 Calculate the square root of the right side: 76131.739544687 Break this problem into two subproblems by setting (x + 75178.97625) equal to 76131.739544687 and -76131.739544687.Subproblem 1
x + 75178.97625 = 76131.739544687 Simplifying x + 75178.97625 = 76131.739544687 Reorder the terms: 75178.97625 + x = 76131.739544687 Solving 75178.97625 + x = 76131.739544687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-75178.97625' to each side of the equation. 75178.97625 + -75178.97625 + x = 76131.739544687 + -75178.97625 Combine like terms: 75178.97625 + -75178.97625 = 0.00000 0.00000 + x = 76131.739544687 + -75178.97625 x = 76131.739544687 + -75178.97625 Combine like terms: 76131.739544687 + -75178.97625 = 952.763294687 x = 952.763294687 Simplifying x = 952.763294687Subproblem 2
x + 75178.97625 = -76131.739544687 Simplifying x + 75178.97625 = -76131.739544687 Reorder the terms: 75178.97625 + x = -76131.739544687 Solving 75178.97625 + x = -76131.739544687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-75178.97625' to each side of the equation. 75178.97625 + -75178.97625 + x = -76131.739544687 + -75178.97625 Combine like terms: 75178.97625 + -75178.97625 = 0.00000 0.00000 + x = -76131.739544687 + -75178.97625 x = -76131.739544687 + -75178.97625 Combine like terms: -76131.739544687 + -75178.97625 = -151310.715794687 x = -151310.715794687 Simplifying x = -151310.715794687Solution
The solution to the problem is based on the solutions from the subproblems. x = {952.763294687, -151310.715794687}
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