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Simplifying x2 + 44x + 306 = 0 Reorder the terms: 306 + 44x + x2 = 0 Solving 306 + 44x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-306' to each side of the equation. 306 + 44x + -306 + x2 = 0 + -306 Reorder the terms: 306 + -306 + 44x + x2 = 0 + -306 Combine like terms: 306 + -306 = 0 0 + 44x + x2 = 0 + -306 44x + x2 = 0 + -306 Combine like terms: 0 + -306 = -306 44x + x2 = -306 The x term is 44x. Take half its coefficient (22). Square it (484) and add it to both sides. Add '484' to each side of the equation. 44x + 484 + x2 = -306 + 484 Reorder the terms: 484 + 44x + x2 = -306 + 484 Combine like terms: -306 + 484 = 178 484 + 44x + x2 = 178 Factor a perfect square on the left side: (x + 22)(x + 22) = 178 Calculate the square root of the right side: 13.341664064 Break this problem into two subproblems by setting (x + 22) equal to 13.341664064 and -13.341664064.Subproblem 1
x + 22 = 13.341664064 Simplifying x + 22 = 13.341664064 Reorder the terms: 22 + x = 13.341664064 Solving 22 + x = 13.341664064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + x = 13.341664064 + -22 Combine like terms: 22 + -22 = 0 0 + x = 13.341664064 + -22 x = 13.341664064 + -22 Combine like terms: 13.341664064 + -22 = -8.658335936 x = -8.658335936 Simplifying x = -8.658335936Subproblem 2
x + 22 = -13.341664064 Simplifying x + 22 = -13.341664064 Reorder the terms: 22 + x = -13.341664064 Solving 22 + x = -13.341664064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + x = -13.341664064 + -22 Combine like terms: 22 + -22 = 0 0 + x = -13.341664064 + -22 x = -13.341664064 + -22 Combine like terms: -13.341664064 + -22 = -35.341664064 x = -35.341664064 Simplifying x = -35.341664064Solution
The solution to the problem is based on the solutions from the subproblems. x = {-8.658335936, -35.341664064}
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