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Simplifying (8 + -1x)(16 + -1x) = 82 Multiply (8 + -1x) * (16 + -1x) (8(16 + -1x) + -1x * (16 + -1x)) = 82 ((16 * 8 + -1x * 8) + -1x * (16 + -1x)) = 82 ((128 + -8x) + -1x * (16 + -1x)) = 82 (128 + -8x + (16 * -1x + -1x * -1x)) = 82 (128 + -8x + (-16x + 1x2)) = 82 Combine like terms: -8x + -16x = -24x (128 + -24x + 1x2) = 82 Solving 128 + -24x + 1x2 = 82 Solving for variable 'x'. Reorder the terms: 128 + -82 + -24x + 1x2 = 82 + -82 Combine like terms: 128 + -82 = 46 46 + -24x + 1x2 = 82 + -82 Combine like terms: 82 + -82 = 0 46 + -24x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-46' to each side of the equation. 46 + -24x + -46 + x2 = 0 + -46 Reorder the terms: 46 + -46 + -24x + x2 = 0 + -46 Combine like terms: 46 + -46 = 0 0 + -24x + x2 = 0 + -46 -24x + x2 = 0 + -46 Combine like terms: 0 + -46 = -46 -24x + x2 = -46 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -46 + 144 Reorder the terms: 144 + -24x + x2 = -46 + 144 Combine like terms: -46 + 144 = 98 144 + -24x + x2 = 98 Factor a perfect square on the left side: (x + -12)(x + -12) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (x + -12) equal to 9.899494937 and -9.899494937.Subproblem 1
x + -12 = 9.899494937 Simplifying x + -12 = 9.899494937 Reorder the terms: -12 + x = 9.899494937 Solving -12 + x = 9.899494937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 9.899494937 + 12 Combine like terms: -12 + 12 = 0 0 + x = 9.899494937 + 12 x = 9.899494937 + 12 Combine like terms: 9.899494937 + 12 = 21.899494937 x = 21.899494937 Simplifying x = 21.899494937Subproblem 2
x + -12 = -9.899494937 Simplifying x + -12 = -9.899494937 Reorder the terms: -12 + x = -9.899494937 Solving -12 + x = -9.899494937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -9.899494937 + 12 Combine like terms: -12 + 12 = 0 0 + x = -9.899494937 + 12 x = -9.899494937 + 12 Combine like terms: -9.899494937 + 12 = 2.100505063 x = 2.100505063 Simplifying x = 2.100505063Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.899494937, 2.100505063}
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