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Simplifying x2 + 37x + 2 = 0 Reorder the terms: 2 + 37x + x2 = 0 Solving 2 + 37x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 37x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 37x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 37x + x2 = 0 + -2 37x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 37x + x2 = -2 The x term is 37x. Take half its coefficient (18.5). Square it (342.25) and add it to both sides. Add '342.25' to each side of the equation. 37x + 342.25 + x2 = -2 + 342.25 Reorder the terms: 342.25 + 37x + x2 = -2 + 342.25 Combine like terms: -2 + 342.25 = 340.25 342.25 + 37x + x2 = 340.25 Factor a perfect square on the left side: (x + 18.5)(x + 18.5) = 340.25 Calculate the square root of the right side: 18.445866746 Break this problem into two subproblems by setting (x + 18.5) equal to 18.445866746 and -18.445866746.Subproblem 1
x + 18.5 = 18.445866746 Simplifying x + 18.5 = 18.445866746 Reorder the terms: 18.5 + x = 18.445866746 Solving 18.5 + x = 18.445866746 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.5' to each side of the equation. 18.5 + -18.5 + x = 18.445866746 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = 18.445866746 + -18.5 x = 18.445866746 + -18.5 Combine like terms: 18.445866746 + -18.5 = -0.054133254 x = -0.054133254 Simplifying x = -0.054133254Subproblem 2
x + 18.5 = -18.445866746 Simplifying x + 18.5 = -18.445866746 Reorder the terms: 18.5 + x = -18.445866746 Solving 18.5 + x = -18.445866746 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.5' to each side of the equation. 18.5 + -18.5 + x = -18.445866746 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = -18.445866746 + -18.5 x = -18.445866746 + -18.5 Combine like terms: -18.445866746 + -18.5 = -36.945866746 x = -36.945866746 Simplifying x = -36.945866746Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.054133254, -36.945866746}
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