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Simplifying x2 + 18x + 41 = 0 Reorder the terms: 41 + 18x + x2 = 0 Solving 41 + 18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + 18x + -41 + x2 = 0 + -41 Reorder the terms: 41 + -41 + 18x + x2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + 18x + x2 = 0 + -41 18x + x2 = 0 + -41 Combine like terms: 0 + -41 = -41 18x + x2 = -41 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = -41 + 81 Reorder the terms: 81 + 18x + x2 = -41 + 81 Combine like terms: -41 + 81 = 40 81 + 18x + x2 = 40 Factor a perfect square on the left side: (x + 9)(x + 9) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (x + 9) equal to 6.32455532 and -6.32455532.Subproblem 1
x + 9 = 6.32455532 Simplifying x + 9 = 6.32455532 Reorder the terms: 9 + x = 6.32455532 Solving 9 + x = 6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 6.32455532 + -9 Combine like terms: 9 + -9 = 0 0 + x = 6.32455532 + -9 x = 6.32455532 + -9 Combine like terms: 6.32455532 + -9 = -2.67544468 x = -2.67544468 Simplifying x = -2.67544468Subproblem 2
x + 9 = -6.32455532 Simplifying x + 9 = -6.32455532 Reorder the terms: 9 + x = -6.32455532 Solving 9 + x = -6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -6.32455532 + -9 Combine like terms: 9 + -9 = 0 0 + x = -6.32455532 + -9 x = -6.32455532 + -9 Combine like terms: -6.32455532 + -9 = -15.32455532 x = -15.32455532 Simplifying x = -15.32455532Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.67544468, -15.32455532}
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