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Simplifying 2x2 + 49x + -246 = 0 Reorder the terms: -246 + 49x + 2x2 = 0 Solving -246 + 49x + 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'. -123 + 24.5x + x2 = 0 Move the constant term to the right: Add '123' to each side of the equation. -123 + 24.5x + 123 + x2 = 0 + 123 Reorder the terms: -123 + 123 + 24.5x + x2 = 0 + 123 Combine like terms: -123 + 123 = 0 0 + 24.5x + x2 = 0 + 123 24.5x + x2 = 0 + 123 Combine like terms: 0 + 123 = 123 24.5x + x2 = 123 The x term is 24.5x. Take half its coefficient (12.25). Square it (150.0625) and add it to both sides. Add '150.0625' to each side of the equation. 24.5x + 150.0625 + x2 = 123 + 150.0625 Reorder the terms: 150.0625 + 24.5x + x2 = 123 + 150.0625 Combine like terms: 123 + 150.0625 = 273.0625 150.0625 + 24.5x + x2 = 273.0625 Factor a perfect square on the left side: (x + 12.25)(x + 12.25) = 273.0625 Calculate the square root of the right side: 16.52460287 Break this problem into two subproblems by setting (x + 12.25) equal to 16.52460287 and -16.52460287.Subproblem 1
x + 12.25 = 16.52460287 Simplifying x + 12.25 = 16.52460287 Reorder the terms: 12.25 + x = 16.52460287 Solving 12.25 + x = 16.52460287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.25' to each side of the equation. 12.25 + -12.25 + x = 16.52460287 + -12.25 Combine like terms: 12.25 + -12.25 = 0.00 0.00 + x = 16.52460287 + -12.25 x = 16.52460287 + -12.25 Combine like terms: 16.52460287 + -12.25 = 4.27460287 x = 4.27460287 Simplifying x = 4.27460287Subproblem 2
x + 12.25 = -16.52460287 Simplifying x + 12.25 = -16.52460287 Reorder the terms: 12.25 + x = -16.52460287 Solving 12.25 + x = -16.52460287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.25' to each side of the equation. 12.25 + -12.25 + x = -16.52460287 + -12.25 Combine like terms: 12.25 + -12.25 = 0.00 0.00 + x = -16.52460287 + -12.25 x = -16.52460287 + -12.25 Combine like terms: -16.52460287 + -12.25 = -28.77460287 x = -28.77460287 Simplifying x = -28.77460287Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.27460287, -28.77460287}
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