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Simplifying -7.7 + 29x + 2x2 = 0 Solving -7.7 + 29x + 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'. -3.85 + 14.5x + x2 = 0 Move the constant term to the right: Add '3.85' to each side of the equation. -3.85 + 14.5x + 3.85 + x2 = 0 + 3.85 Reorder the terms: -3.85 + 3.85 + 14.5x + x2 = 0 + 3.85 Combine like terms: -3.85 + 3.85 = 0.00 0.00 + 14.5x + x2 = 0 + 3.85 14.5x + x2 = 0 + 3.85 Combine like terms: 0 + 3.85 = 3.85 14.5x + x2 = 3.85 The x term is 14.5x. Take half its coefficient (7.25). Square it (52.5625) and add it to both sides. Add '52.5625' to each side of the equation. 14.5x + 52.5625 + x2 = 3.85 + 52.5625 Reorder the terms: 52.5625 + 14.5x + x2 = 3.85 + 52.5625 Combine like terms: 3.85 + 52.5625 = 56.4125 52.5625 + 14.5x + x2 = 56.4125 Factor a perfect square on the left side: (x + 7.25)(x + 7.25) = 56.4125 Calculate the square root of the right side: 7.510825521 Break this problem into two subproblems by setting (x + 7.25) equal to 7.510825521 and -7.510825521.Subproblem 1
x + 7.25 = 7.510825521 Simplifying x + 7.25 = 7.510825521 Reorder the terms: 7.25 + x = 7.510825521 Solving 7.25 + x = 7.510825521 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + x = 7.510825521 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + x = 7.510825521 + -7.25 x = 7.510825521 + -7.25 Combine like terms: 7.510825521 + -7.25 = 0.260825521 x = 0.260825521 Simplifying x = 0.260825521Subproblem 2
x + 7.25 = -7.510825521 Simplifying x + 7.25 = -7.510825521 Reorder the terms: 7.25 + x = -7.510825521 Solving 7.25 + x = -7.510825521 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + x = -7.510825521 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + x = -7.510825521 + -7.25 x = -7.510825521 + -7.25 Combine like terms: -7.510825521 + -7.25 = -14.760825521 x = -14.760825521 Simplifying x = -14.760825521Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.260825521, -14.760825521}
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