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Simplifying x2 + 11x + -11 = 0 Reorder the terms: -11 + 11x + x2 = 0 Solving -11 + 11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 11x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 11x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 11x + x2 = 0 + 11 11x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 11x + x2 = 11 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 = 11 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 11 + 30.25 Combine like terms: 11 + 30.25 = 41.25 30.25 + 11x + x2 = 41.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 41.25 Calculate the square root of the right side: 6.422616289 Break this problem into two subproblems by setting (x + 5.5) equal to 6.422616289 and -6.422616289.Subproblem 1
x + 5.5 = 6.422616289 Simplifying x + 5.5 = 6.422616289 Reorder the terms: 5.5 + x = 6.422616289 Solving 5.5 + x = 6.422616289 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 = 6.422616289 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 6.422616289 + -5.5 x = 6.422616289 + -5.5 Combine like terms: 6.422616289 + -5.5 = 0.922616289 x = 0.922616289 Simplifying x = 0.922616289Subproblem 2
x + 5.5 = -6.422616289 Simplifying x + 5.5 = -6.422616289 Reorder the terms: 5.5 + x = -6.422616289 Solving 5.5 + x = -6.422616289 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 = -6.422616289 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -6.422616289 + -5.5 x = -6.422616289 + -5.5 Combine like terms: -6.422616289 + -5.5 = -11.922616289 x = -11.922616289 Simplifying x = -11.922616289Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.922616289, -11.922616289}
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