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Simplifying 20x2 + 61x + 35 = 0 Reorder the terms: 35 + 61x + 20x2 = 0 Solving 35 + 61x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 1.75 + 3.05x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + 3.05x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + 3.05x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + 3.05x + x2 = 0 + -1.75 3.05x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 3.05x + x2 = -1.75 The x term is 3.05x. Take half its coefficient (1.525). Square it (2.325625) and add it to both sides. Add '2.325625' to each side of the equation. 3.05x + 2.325625 + x2 = -1.75 + 2.325625 Reorder the terms: 2.325625 + 3.05x + x2 = -1.75 + 2.325625 Combine like terms: -1.75 + 2.325625 = 0.575625 2.325625 + 3.05x + x2 = 0.575625 Factor a perfect square on the left side: (x + 1.525)(x + 1.525) = 0.575625 Calculate the square root of the right side: 0.758699545 Break this problem into two subproblems by setting (x + 1.525) equal to 0.758699545 and -0.758699545.Subproblem 1
x + 1.525 = 0.758699545 Simplifying x + 1.525 = 0.758699545 Reorder the terms: 1.525 + x = 0.758699545 Solving 1.525 + x = 0.758699545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.525' to each side of the equation. 1.525 + -1.525 + x = 0.758699545 + -1.525 Combine like terms: 1.525 + -1.525 = 0.000 0.000 + x = 0.758699545 + -1.525 x = 0.758699545 + -1.525 Combine like terms: 0.758699545 + -1.525 = -0.766300455 x = -0.766300455 Simplifying x = -0.766300455Subproblem 2
x + 1.525 = -0.758699545 Simplifying x + 1.525 = -0.758699545 Reorder the terms: 1.525 + x = -0.758699545 Solving 1.525 + x = -0.758699545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.525' to each side of the equation. 1.525 + -1.525 + x = -0.758699545 + -1.525 Combine like terms: 1.525 + -1.525 = 0.000 0.000 + x = -0.758699545 + -1.525 x = -0.758699545 + -1.525 Combine like terms: -0.758699545 + -1.525 = -2.283699545 x = -2.283699545 Simplifying x = -2.283699545Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.766300455, -2.283699545}
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