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Simplifying (x + -329)(x + 92) = x + 3814 Reorder the terms: (-329 + x)(x + 92) = x + 3814 Reorder the terms: (-329 + x)(92 + x) = x + 3814 Multiply (-329 + x) * (92 + x) (-329(92 + x) + x(92 + x)) = x + 3814 ((92 * -329 + x * -329) + x(92 + x)) = x + 3814 ((-30268 + -329x) + x(92 + x)) = x + 3814 (-30268 + -329x + (92 * x + x * x)) = x + 3814 (-30268 + -329x + (92x + x2)) = x + 3814 Combine like terms: -329x + 92x = -237x (-30268 + -237x + x2) = x + 3814 Reorder the terms: -30268 + -237x + x2 = 3814 + x Solving -30268 + -237x + x2 = 3814 + x Solving for variable 'x'. Reorder the terms: -30268 + -3814 + -237x + -1x + x2 = 3814 + x + -3814 + -1x Combine like terms: -30268 + -3814 = -34082 -34082 + -237x + -1x + x2 = 3814 + x + -3814 + -1x Combine like terms: -237x + -1x = -238x -34082 + -238x + x2 = 3814 + x + -3814 + -1x Reorder the terms: -34082 + -238x + x2 = 3814 + -3814 + x + -1x Combine like terms: 3814 + -3814 = 0 -34082 + -238x + x2 = 0 + x + -1x -34082 + -238x + x2 = x + -1x Combine like terms: x + -1x = 0 -34082 + -238x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '34082' to each side of the equation. -34082 + -238x + 34082 + x2 = 0 + 34082 Reorder the terms: -34082 + 34082 + -238x + x2 = 0 + 34082 Combine like terms: -34082 + 34082 = 0 0 + -238x + x2 = 0 + 34082 -238x + x2 = 0 + 34082 Combine like terms: 0 + 34082 = 34082 -238x + x2 = 34082 The x term is -238x. Take half its coefficient (-119). Square it (14161) and add it to both sides. Add '14161' to each side of the equation. -238x + 14161 + x2 = 34082 + 14161 Reorder the terms: 14161 + -238x + x2 = 34082 + 14161 Combine like terms: 34082 + 14161 = 48243 14161 + -238x + x2 = 48243 Factor a perfect square on the left side: (x + -119)(x + -119) = 48243 Calculate the square root of the right side: 219.642891986 Break this problem into two subproblems by setting (x + -119) equal to 219.642891986 and -219.642891986.Subproblem 1
x + -119 = 219.642891986 Simplifying x + -119 = 219.642891986 Reorder the terms: -119 + x = 219.642891986 Solving -119 + x = 219.642891986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '119' to each side of the equation. -119 + 119 + x = 219.642891986 + 119 Combine like terms: -119 + 119 = 0 0 + x = 219.642891986 + 119 x = 219.642891986 + 119 Combine like terms: 219.642891986 + 119 = 338.642891986 x = 338.642891986 Simplifying x = 338.642891986Subproblem 2
x + -119 = -219.642891986 Simplifying x + -119 = -219.642891986 Reorder the terms: -119 + x = -219.642891986 Solving -119 + x = -219.642891986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '119' to each side of the equation. -119 + 119 + x = -219.642891986 + 119 Combine like terms: -119 + 119 = 0 0 + x = -219.642891986 + 119 x = -219.642891986 + 119 Combine like terms: -219.642891986 + 119 = -100.642891986 x = -100.642891986 Simplifying x = -100.642891986Solution
The solution to the problem is based on the solutions from the subproblems. x = {338.642891986, -100.642891986}
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