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Simplifying x2 + -6x + 9 = 44 + -11x Reorder the terms: 9 + -6x + x2 = 44 + -11x Solving 9 + -6x + x2 = 44 + -11x Solving for variable 'x'. Reorder the terms: 9 + -44 + -6x + 11x + x2 = 44 + -11x + -44 + 11x Combine like terms: 9 + -44 = -35 -35 + -6x + 11x + x2 = 44 + -11x + -44 + 11x Combine like terms: -6x + 11x = 5x -35 + 5x + x2 = 44 + -11x + -44 + 11x Reorder the terms: -35 + 5x + x2 = 44 + -44 + -11x + 11x Combine like terms: 44 + -44 = 0 -35 + 5x + x2 = 0 + -11x + 11x -35 + 5x + x2 = -11x + 11x Combine like terms: -11x + 11x = 0 -35 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + 5x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + 5x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 5x + x2 = 0 + 35 5x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 5x + x2 = 35 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 35 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 35 + 6.25 Combine like terms: 35 + 6.25 = 41.25 6.25 + 5x + x2 = 41.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 41.25 Calculate the square root of the right side: 6.422616289 Break this problem into two subproblems by setting (x + 2.5) equal to 6.422616289 and -6.422616289.Subproblem 1
x + 2.5 = 6.422616289 Simplifying x + 2.5 = 6.422616289 Reorder the terms: 2.5 + x = 6.422616289 Solving 2.5 + x = 6.422616289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 6.422616289 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 6.422616289 + -2.5 x = 6.422616289 + -2.5 Combine like terms: 6.422616289 + -2.5 = 3.922616289 x = 3.922616289 Simplifying x = 3.922616289Subproblem 2
x + 2.5 = -6.422616289 Simplifying x + 2.5 = -6.422616289 Reorder the terms: 2.5 + x = -6.422616289 Solving 2.5 + x = -6.422616289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -6.422616289 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -6.422616289 + -2.5 x = -6.422616289 + -2.5 Combine like terms: -6.422616289 + -2.5 = -8.922616289 x = -8.922616289 Simplifying x = -8.922616289Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.922616289, -8.922616289}
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