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Simplifying x2 + 16x + 41 = 0 Reorder the terms: 41 + 16x + x2 = 0 Solving 41 + 16x + 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 + 16x + -41 + x2 = 0 + -41 Reorder the terms: 41 + -41 + 16x + x2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + 16x + x2 = 0 + -41 16x + x2 = 0 + -41 Combine like terms: 0 + -41 = -41 16x + x2 = -41 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = -41 + 64 Reorder the terms: 64 + 16x + x2 = -41 + 64 Combine like terms: -41 + 64 = 23 64 + 16x + x2 = 23 Factor a perfect square on the left side: (x + 8)(x + 8) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (x + 8) equal to 4.795831523 and -4.795831523.Subproblem 1
x + 8 = 4.795831523 Simplifying x + 8 = 4.795831523 Reorder the terms: 8 + x = 4.795831523 Solving 8 + x = 4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 4.795831523 + -8 Combine like terms: 8 + -8 = 0 0 + x = 4.795831523 + -8 x = 4.795831523 + -8 Combine like terms: 4.795831523 + -8 = -3.204168477 x = -3.204168477 Simplifying x = -3.204168477Subproblem 2
x + 8 = -4.795831523 Simplifying x + 8 = -4.795831523 Reorder the terms: 8 + x = -4.795831523 Solving 8 + x = -4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -4.795831523 + -8 Combine like terms: 8 + -8 = 0 0 + x = -4.795831523 + -8 x = -4.795831523 + -8 Combine like terms: -4.795831523 + -8 = -12.795831523 x = -12.795831523 Simplifying x = -12.795831523Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.204168477, -12.795831523}
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