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Simplifying x2 + 38x + 20 = 0 Reorder the terms: 20 + 38x + x2 = 0 Solving 20 + 38x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 38x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + 38x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 38x + x2 = 0 + -20 38x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 38x + x2 = -20 The x term is 38x. Take half its coefficient (19). Square it (361) and add it to both sides. Add '361' to each side of the equation. 38x + 361 + x2 = -20 + 361 Reorder the terms: 361 + 38x + x2 = -20 + 361 Combine like terms: -20 + 361 = 341 361 + 38x + x2 = 341 Factor a perfect square on the left side: (x + 19)(x + 19) = 341 Calculate the square root of the right side: 18.466185313 Break this problem into two subproblems by setting (x + 19) equal to 18.466185313 and -18.466185313.Subproblem 1
x + 19 = 18.466185313 Simplifying x + 19 = 18.466185313 Reorder the terms: 19 + x = 18.466185313 Solving 19 + x = 18.466185313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + x = 18.466185313 + -19 Combine like terms: 19 + -19 = 0 0 + x = 18.466185313 + -19 x = 18.466185313 + -19 Combine like terms: 18.466185313 + -19 = -0.533814687 x = -0.533814687 Simplifying x = -0.533814687Subproblem 2
x + 19 = -18.466185313 Simplifying x + 19 = -18.466185313 Reorder the terms: 19 + x = -18.466185313 Solving 19 + x = -18.466185313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + x = -18.466185313 + -19 Combine like terms: 19 + -19 = 0 0 + x = -18.466185313 + -19 x = -18.466185313 + -19 Combine like terms: -18.466185313 + -19 = -37.466185313 x = -37.466185313 Simplifying x = -37.466185313Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.533814687, -37.466185313}
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