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Simplifying 2x2 + 65x + -1250 = 0 Reorder the terms: -1250 + 65x + 2x2 = 0 Solving -1250 + 65x + 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'. -625 + 32.5x + x2 = 0 Move the constant term to the right: Add '625' to each side of the equation. -625 + 32.5x + 625 + x2 = 0 + 625 Reorder the terms: -625 + 625 + 32.5x + x2 = 0 + 625 Combine like terms: -625 + 625 = 0 0 + 32.5x + x2 = 0 + 625 32.5x + x2 = 0 + 625 Combine like terms: 0 + 625 = 625 32.5x + x2 = 625 The x term is 32.5x. Take half its coefficient (16.25). Square it (264.0625) and add it to both sides. Add '264.0625' to each side of the equation. 32.5x + 264.0625 + x2 = 625 + 264.0625 Reorder the terms: 264.0625 + 32.5x + x2 = 625 + 264.0625 Combine like terms: 625 + 264.0625 = 889.0625 264.0625 + 32.5x + x2 = 889.0625 Factor a perfect square on the left side: (x + 16.25)(x + 16.25) = 889.0625 Calculate the square root of the right side: 29.817151105 Break this problem into two subproblems by setting (x + 16.25) equal to 29.817151105 and -29.817151105.Subproblem 1
x + 16.25 = 29.817151105 Simplifying x + 16.25 = 29.817151105 Reorder the terms: 16.25 + x = 29.817151105 Solving 16.25 + x = 29.817151105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.25' to each side of the equation. 16.25 + -16.25 + x = 29.817151105 + -16.25 Combine like terms: 16.25 + -16.25 = 0.00 0.00 + x = 29.817151105 + -16.25 x = 29.817151105 + -16.25 Combine like terms: 29.817151105 + -16.25 = 13.567151105 x = 13.567151105 Simplifying x = 13.567151105Subproblem 2
x + 16.25 = -29.817151105 Simplifying x + 16.25 = -29.817151105 Reorder the terms: 16.25 + x = -29.817151105 Solving 16.25 + x = -29.817151105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.25' to each side of the equation. 16.25 + -16.25 + x = -29.817151105 + -16.25 Combine like terms: 16.25 + -16.25 = 0.00 0.00 + x = -29.817151105 + -16.25 x = -29.817151105 + -16.25 Combine like terms: -29.817151105 + -16.25 = -46.067151105 x = -46.067151105 Simplifying x = -46.067151105Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.567151105, -46.067151105}
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