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Simplifying x2 + 38x + 183 = 0 Reorder the terms: 183 + 38x + x2 = 0 Solving 183 + 38x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-183' to each side of the equation. 183 + 38x + -183 + x2 = 0 + -183 Reorder the terms: 183 + -183 + 38x + x2 = 0 + -183 Combine like terms: 183 + -183 = 0 0 + 38x + x2 = 0 + -183 38x + x2 = 0 + -183 Combine like terms: 0 + -183 = -183 38x + x2 = -183 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 = -183 + 361 Reorder the terms: 361 + 38x + x2 = -183 + 361 Combine like terms: -183 + 361 = 178 361 + 38x + x2 = 178 Factor a perfect square on the left side: (x + 19)(x + 19) = 178 Calculate the square root of the right side: 13.341664064 Break this problem into two subproblems by setting (x + 19) equal to 13.341664064 and -13.341664064.Subproblem 1
x + 19 = 13.341664064 Simplifying x + 19 = 13.341664064 Reorder the terms: 19 + x = 13.341664064 Solving 19 + x = 13.341664064 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 = 13.341664064 + -19 Combine like terms: 19 + -19 = 0 0 + x = 13.341664064 + -19 x = 13.341664064 + -19 Combine like terms: 13.341664064 + -19 = -5.658335936 x = -5.658335936 Simplifying x = -5.658335936Subproblem 2
x + 19 = -13.341664064 Simplifying x + 19 = -13.341664064 Reorder the terms: 19 + x = -13.341664064 Solving 19 + x = -13.341664064 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 = -13.341664064 + -19 Combine like terms: 19 + -19 = 0 0 + x = -13.341664064 + -19 x = -13.341664064 + -19 Combine like terms: -13.341664064 + -19 = -32.341664064 x = -32.341664064 Simplifying x = -32.341664064Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.658335936, -32.341664064}
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