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Simplifying 209960735x2 + 31569266222.9275x + -30268631606950 = 0 Reorder the terms: -30268631606950 + 31569266222.9275x + 209960735x2 = 0 Solving -30268631606950 + 31569266222.9275x + 209960735x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 209960735 the coefficient of the squared term: Divide each side by '209960735'. -144163.2961 + 150.3579525x + x2 = 0 Move the constant term to the right: Add '144163.2961' to each side of the equation. -144163.2961 + 150.3579525x + 144163.2961 + x2 = 0 + 144163.2961 Reorder the terms: -144163.2961 + 144163.2961 + 150.3579525x + x2 = 0 + 144163.2961 Combine like terms: -144163.2961 + 144163.2961 = 0.0000 0.0000 + 150.3579525x + x2 = 0 + 144163.2961 150.3579525x + x2 = 0 + 144163.2961 Combine like terms: 0 + 144163.2961 = 144163.2961 150.3579525x + x2 = 144163.2961 The x term is 150.3579525x. Take half its coefficient (75.17897625). Square it (5651.878470) and add it to both sides. Add '5651.878470' to each side of the equation. 150.3579525x + 5651.878470 + x2 = 144163.2961 + 5651.878470 Reorder the terms: 5651.878470 + 150.3579525x + x2 = 144163.2961 + 5651.878470 Combine like terms: 144163.2961 + 5651.878470 = 149815.17457 5651.878470 + 150.3579525x + x2 = 149815.17457 Factor a perfect square on the left side: (x + 75.17897625)(x + 75.17897625) = 149815.17457 Calculate the square root of the right side: 387.05965247 Break this problem into two subproblems by setting (x + 75.17897625) equal to 387.05965247 and -387.05965247.Subproblem 1
x + 75.17897625 = 387.05965247 Simplifying x + 75.17897625 = 387.05965247 Reorder the terms: 75.17897625 + x = 387.05965247 Solving 75.17897625 + x = 387.05965247 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-75.17897625' to each side of the equation. 75.17897625 + -75.17897625 + x = 387.05965247 + -75.17897625 Combine like terms: 75.17897625 + -75.17897625 = 0.00000000 0.00000000 + x = 387.05965247 + -75.17897625 x = 387.05965247 + -75.17897625 Combine like terms: 387.05965247 + -75.17897625 = 311.88067622 x = 311.88067622 Simplifying x = 311.88067622Subproblem 2
x + 75.17897625 = -387.05965247 Simplifying x + 75.17897625 = -387.05965247 Reorder the terms: 75.17897625 + x = -387.05965247 Solving 75.17897625 + x = -387.05965247 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-75.17897625' to each side of the equation. 75.17897625 + -75.17897625 + x = -387.05965247 + -75.17897625 Combine like terms: 75.17897625 + -75.17897625 = 0.00000000 0.00000000 + x = -387.05965247 + -75.17897625 x = -387.05965247 + -75.17897625 Combine like terms: -387.05965247 + -75.17897625 = -462.23862872 x = -462.23862872 Simplifying x = -462.23862872Solution
The solution to the problem is based on the solutions from the subproblems. x = {311.88067622, -462.23862872}
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