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Simplifying 2x2 + -25x + 37 = 0 Reorder the terms: 37 + -25x + 2x2 = 0 Solving 37 + -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'. 18.5 + -12.5x + x2 = 0 Move the constant term to the right: Add '-18.5' to each side of the equation. 18.5 + -12.5x + -18.5 + x2 = 0 + -18.5 Reorder the terms: 18.5 + -18.5 + -12.5x + x2 = 0 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + -12.5x + x2 = 0 + -18.5 -12.5x + x2 = 0 + -18.5 Combine like terms: 0 + -18.5 = -18.5 -12.5x + x2 = -18.5 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 = -18.5 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = -18.5 + 39.0625 Combine like terms: -18.5 + 39.0625 = 20.5625 39.0625 + -12.5x + x2 = 20.5625 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 20.5625 Calculate the square root of the right side: 4.534589287 Break this problem into two subproblems by setting (x + -6.25) equal to 4.534589287 and -4.534589287.Subproblem 1
x + -6.25 = 4.534589287 Simplifying x + -6.25 = 4.534589287 Reorder the terms: -6.25 + x = 4.534589287 Solving -6.25 + x = 4.534589287 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 = 4.534589287 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 4.534589287 + 6.25 x = 4.534589287 + 6.25 Combine like terms: 4.534589287 + 6.25 = 10.784589287 x = 10.784589287 Simplifying x = 10.784589287Subproblem 2
x + -6.25 = -4.534589287 Simplifying x + -6.25 = -4.534589287 Reorder the terms: -6.25 + x = -4.534589287 Solving -6.25 + x = -4.534589287 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 = -4.534589287 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -4.534589287 + 6.25 x = -4.534589287 + 6.25 Combine like terms: -4.534589287 + 6.25 = 1.715410713 x = 1.715410713 Simplifying x = 1.715410713Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.784589287, 1.715410713}
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