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Simplifying (x + 2)(x + -91) = 182 Reorder the terms: (2 + x)(x + -91) = 182 Reorder the terms: (2 + x)(-91 + x) = 182 Multiply (2 + x) * (-91 + x) (2(-91 + x) + x(-91 + x)) = 182 ((-91 * 2 + x * 2) + x(-91 + x)) = 182 ((-182 + 2x) + x(-91 + x)) = 182 (-182 + 2x + (-91 * x + x * x)) = 182 (-182 + 2x + (-91x + x2)) = 182 Combine like terms: 2x + -91x = -89x (-182 + -89x + x2) = 182 Solving -182 + -89x + x2 = 182 Solving for variable 'x'. Reorder the terms: -182 + -182 + -89x + x2 = 182 + -182 Combine like terms: -182 + -182 = -364 -364 + -89x + x2 = 182 + -182 Combine like terms: 182 + -182 = 0 -364 + -89x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '364' to each side of the equation. -364 + -89x + 364 + x2 = 0 + 364 Reorder the terms: -364 + 364 + -89x + x2 = 0 + 364 Combine like terms: -364 + 364 = 0 0 + -89x + x2 = 0 + 364 -89x + x2 = 0 + 364 Combine like terms: 0 + 364 = 364 -89x + x2 = 364 The x term is -89x. Take half its coefficient (-44.5). Square it (1980.25) and add it to both sides. Add '1980.25' to each side of the equation. -89x + 1980.25 + x2 = 364 + 1980.25 Reorder the terms: 1980.25 + -89x + x2 = 364 + 1980.25 Combine like terms: 364 + 1980.25 = 2344.25 1980.25 + -89x + x2 = 2344.25 Factor a perfect square on the left side: (x + -44.5)(x + -44.5) = 2344.25 Calculate the square root of the right side: 48.41745553 Break this problem into two subproblems by setting (x + -44.5) equal to 48.41745553 and -48.41745553.Subproblem 1
x + -44.5 = 48.41745553 Simplifying x + -44.5 = 48.41745553 Reorder the terms: -44.5 + x = 48.41745553 Solving -44.5 + x = 48.41745553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '44.5' to each side of the equation. -44.5 + 44.5 + x = 48.41745553 + 44.5 Combine like terms: -44.5 + 44.5 = 0.0 0.0 + x = 48.41745553 + 44.5 x = 48.41745553 + 44.5 Combine like terms: 48.41745553 + 44.5 = 92.91745553 x = 92.91745553 Simplifying x = 92.91745553Subproblem 2
x + -44.5 = -48.41745553 Simplifying x + -44.5 = -48.41745553 Reorder the terms: -44.5 + x = -48.41745553 Solving -44.5 + x = -48.41745553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '44.5' to each side of the equation. -44.5 + 44.5 + x = -48.41745553 + 44.5 Combine like terms: -44.5 + 44.5 = 0.0 0.0 + x = -48.41745553 + 44.5 x = -48.41745553 + 44.5 Combine like terms: -48.41745553 + 44.5 = -3.91745553 x = -3.91745553 Simplifying x = -3.91745553Solution
The solution to the problem is based on the solutions from the subproblems. x = {92.91745553, -3.91745553}
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