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Simplifying 2x2 + -25x + -209 = 0 Reorder the terms: -209 + -25x + 2x2 = 0 Solving -209 + -25x + 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'. -104.5 + -12.5x + x2 = 0 Move the constant term to the right: Add '104.5' to each side of the equation. -104.5 + -12.5x + 104.5 + x2 = 0 + 104.5 Reorder the terms: -104.5 + 104.5 + -12.5x + x2 = 0 + 104.5 Combine like terms: -104.5 + 104.5 = 0.0 0.0 + -12.5x + x2 = 0 + 104.5 -12.5x + x2 = 0 + 104.5 Combine like terms: 0 + 104.5 = 104.5 -12.5x + x2 = 104.5 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = 104.5 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = 104.5 + 39.0625 Combine like terms: 104.5 + 39.0625 = 143.5625 39.0625 + -12.5x + x2 = 143.5625 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 143.5625 Calculate the square root of the right side: 11.981756966 Break this problem into two subproblems by setting (x + -6.25) equal to 11.981756966 and -11.981756966.Subproblem 1
x + -6.25 = 11.981756966 Simplifying x + -6.25 = 11.981756966 Reorder the terms: -6.25 + x = 11.981756966 Solving -6.25 + x = 11.981756966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 11.981756966 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 11.981756966 + 6.25 x = 11.981756966 + 6.25 Combine like terms: 11.981756966 + 6.25 = 18.231756966 x = 18.231756966 Simplifying x = 18.231756966Subproblem 2
x + -6.25 = -11.981756966 Simplifying x + -6.25 = -11.981756966 Reorder the terms: -6.25 + x = -11.981756966 Solving -6.25 + x = -11.981756966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -11.981756966 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -11.981756966 + 6.25 x = -11.981756966 + 6.25 Combine like terms: -11.981756966 + 6.25 = -5.731756966 x = -5.731756966 Simplifying x = -5.731756966Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.231756966, -5.731756966}
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