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Simplifying 2x2 + 18.3x + -226.1 = 0 Reorder the terms: -226.1 + 18.3x + 2x2 = 0 Solving -226.1 + 18.3x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -113.05 + 9.15x + x2 = 0 Move the constant term to the right: Add '113.05' to each side of the equation. -113.05 + 9.15x + 113.05 + x2 = 0 + 113.05 Reorder the terms: -113.05 + 113.05 + 9.15x + x2 = 0 + 113.05 Combine like terms: -113.05 + 113.05 = 0.00 0.00 + 9.15x + x2 = 0 + 113.05 9.15x + x2 = 0 + 113.05 Combine like terms: 0 + 113.05 = 113.05 9.15x + x2 = 113.05 The x term is 9.15x. Take half its coefficient (4.575). Square it (20.930625) and add it to both sides. Add '20.930625' to each side of the equation. 9.15x + 20.930625 + x2 = 113.05 + 20.930625 Reorder the terms: 20.930625 + 9.15x + x2 = 113.05 + 20.930625 Combine like terms: 113.05 + 20.930625 = 133.980625 20.930625 + 9.15x + x2 = 133.980625 Factor a perfect square on the left side: (x + 4.575)(x + 4.575) = 133.980625 Calculate the square root of the right side: 11.575 Break this problem into two subproblems by setting (x + 4.575) equal to 11.575 and -11.575.Subproblem 1
x + 4.575 = 11.575 Simplifying x + 4.575 = 11.575 Reorder the terms: 4.575 + x = 11.575 Solving 4.575 + x = 11.575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.575' to each side of the equation. 4.575 + -4.575 + x = 11.575 + -4.575 Combine like terms: 4.575 + -4.575 = 0.000 0.000 + x = 11.575 + -4.575 x = 11.575 + -4.575 Combine like terms: 11.575 + -4.575 = 7 x = 7 Simplifying x = 7Subproblem 2
x + 4.575 = -11.575 Simplifying x + 4.575 = -11.575 Reorder the terms: 4.575 + x = -11.575 Solving 4.575 + x = -11.575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.575' to each side of the equation. 4.575 + -4.575 + x = -11.575 + -4.575 Combine like terms: 4.575 + -4.575 = 0.000 0.000 + x = -11.575 + -4.575 x = -11.575 + -4.575 Combine like terms: -11.575 + -4.575 = -16.15 x = -16.15 Simplifying x = -16.15Solution
The solution to the problem is based on the solutions from the subproblems. x = {7, -16.15}
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