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Simplifying 18x2 + 900x + -7015909 = 0 Reorder the terms: -7015909 + 900x + 18x2 = 0 Solving -7015909 + 900x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -389772.7222 + 50x + x2 = 0 Move the constant term to the right: Add '389772.7222' to each side of the equation. -389772.7222 + 50x + 389772.7222 + x2 = 0 + 389772.7222 Reorder the terms: -389772.7222 + 389772.7222 + 50x + x2 = 0 + 389772.7222 Combine like terms: -389772.7222 + 389772.7222 = 0.0000 0.0000 + 50x + x2 = 0 + 389772.7222 50x + x2 = 0 + 389772.7222 Combine like terms: 0 + 389772.7222 = 389772.7222 50x + x2 = 389772.7222 The x term is 50x. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50x + 625 + x2 = 389772.7222 + 625 Reorder the terms: 625 + 50x + x2 = 389772.7222 + 625 Combine like terms: 389772.7222 + 625 = 390397.7222 625 + 50x + x2 = 390397.7222 Factor a perfect square on the left side: (x + 25)(x + 25) = 390397.7222 Calculate the square root of the right side: 624.818151305 Break this problem into two subproblems by setting (x + 25) equal to 624.818151305 and -624.818151305.Subproblem 1
x + 25 = 624.818151305 Simplifying x + 25 = 624.818151305 Reorder the terms: 25 + x = 624.818151305 Solving 25 + x = 624.818151305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 624.818151305 + -25 Combine like terms: 25 + -25 = 0 0 + x = 624.818151305 + -25 x = 624.818151305 + -25 Combine like terms: 624.818151305 + -25 = 599.818151305 x = 599.818151305 Simplifying x = 599.818151305Subproblem 2
x + 25 = -624.818151305 Simplifying x + 25 = -624.818151305 Reorder the terms: 25 + x = -624.818151305 Solving 25 + x = -624.818151305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = -624.818151305 + -25 Combine like terms: 25 + -25 = 0 0 + x = -624.818151305 + -25 x = -624.818151305 + -25 Combine like terms: -624.818151305 + -25 = -649.818151305 x = -649.818151305 Simplifying x = -649.818151305Solution
The solution to the problem is based on the solutions from the subproblems. x = {599.818151305, -649.818151305}
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