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Simplifying x2 + 11x + 29 = 0 Reorder the terms: 29 + 11x + x2 = 0 Solving 29 + 11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + 11x + -29 + x2 = 0 + -29 Reorder the terms: 29 + -29 + 11x + x2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 11x + x2 = 0 + -29 11x + x2 = 0 + -29 Combine like terms: 0 + -29 = -29 11x + x2 = -29 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = -29 + 30.25 Reorder the terms: 30.25 + 11x + x2 = -29 + 30.25 Combine like terms: -29 + 30.25 = 1.25 30.25 + 11x + x2 = 1.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + 5.5) equal to 1.118033989 and -1.118033989.Subproblem 1
x + 5.5 = 1.118033989 Simplifying x + 5.5 = 1.118033989 Reorder the terms: 5.5 + x = 1.118033989 Solving 5.5 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 1.118033989 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 1.118033989 + -5.5 x = 1.118033989 + -5.5 Combine like terms: 1.118033989 + -5.5 = -4.381966011 x = -4.381966011 Simplifying x = -4.381966011Subproblem 2
x + 5.5 = -1.118033989 Simplifying x + 5.5 = -1.118033989 Reorder the terms: 5.5 + x = -1.118033989 Solving 5.5 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -1.118033989 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -1.118033989 + -5.5 x = -1.118033989 + -5.5 Combine like terms: -1.118033989 + -5.5 = -6.618033989 x = -6.618033989 Simplifying x = -6.618033989Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.381966011, -6.618033989}
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