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Simplifying x2 + 38x + 195 = 0 Reorder the terms: 195 + 38x + x2 = 0 Solving 195 + 38x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-195' to each side of the equation. 195 + 38x + -195 + x2 = 0 + -195 Reorder the terms: 195 + -195 + 38x + x2 = 0 + -195 Combine like terms: 195 + -195 = 0 0 + 38x + x2 = 0 + -195 38x + x2 = 0 + -195 Combine like terms: 0 + -195 = -195 38x + x2 = -195 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 = -195 + 361 Reorder the terms: 361 + 38x + x2 = -195 + 361 Combine like terms: -195 + 361 = 166 361 + 38x + x2 = 166 Factor a perfect square on the left side: (x + 19)(x + 19) = 166 Calculate the square root of the right side: 12.884098727 Break this problem into two subproblems by setting (x + 19) equal to 12.884098727 and -12.884098727.Subproblem 1
x + 19 = 12.884098727 Simplifying x + 19 = 12.884098727 Reorder the terms: 19 + x = 12.884098727 Solving 19 + x = 12.884098727 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 = 12.884098727 + -19 Combine like terms: 19 + -19 = 0 0 + x = 12.884098727 + -19 x = 12.884098727 + -19 Combine like terms: 12.884098727 + -19 = -6.115901273 x = -6.115901273 Simplifying x = -6.115901273Subproblem 2
x + 19 = -12.884098727 Simplifying x + 19 = -12.884098727 Reorder the terms: 19 + x = -12.884098727 Solving 19 + x = -12.884098727 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 = -12.884098727 + -19 Combine like terms: 19 + -19 = 0 0 + x = -12.884098727 + -19 x = -12.884098727 + -19 Combine like terms: -12.884098727 + -19 = -31.884098727 x = -31.884098727 Simplifying x = -31.884098727Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.115901273, -31.884098727}
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