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Simplifying x(82.75 + -1x) = 1668 (82.75 * x + -1x * x) = 1668 (82.75x + -1x2) = 1668 Solving 82.75x + -1x2 = 1668 Solving for variable 'x'. Reorder the terms: -1668 + 82.75x + -1x2 = 1668 + -1668 Combine like terms: 1668 + -1668 = 0 -1668 + 82.75x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1668 + -82.75x + x2 = 0 Move the constant term to the right: Add '-1668' to each side of the equation. 1668 + -82.75x + -1668 + x2 = 0 + -1668 Reorder the terms: 1668 + -1668 + -82.75x + x2 = 0 + -1668 Combine like terms: 1668 + -1668 = 0 0 + -82.75x + x2 = 0 + -1668 -82.75x + x2 = 0 + -1668 Combine like terms: 0 + -1668 = -1668 -82.75x + x2 = -1668 The x term is -82.75x. Take half its coefficient (-41.375). Square it (1711.890625) and add it to both sides. Add '1711.890625' to each side of the equation. -82.75x + 1711.890625 + x2 = -1668 + 1711.890625 Reorder the terms: 1711.890625 + -82.75x + x2 = -1668 + 1711.890625 Combine like terms: -1668 + 1711.890625 = 43.890625 1711.890625 + -82.75x + x2 = 43.890625 Factor a perfect square on the left side: (x + -41.375)(x + -41.375) = 43.890625 Calculate the square root of the right side: 6.625 Break this problem into two subproblems by setting (x + -41.375) equal to 6.625 and -6.625.Subproblem 1
x + -41.375 = 6.625 Simplifying x + -41.375 = 6.625 Reorder the terms: -41.375 + x = 6.625 Solving -41.375 + x = 6.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '41.375' to each side of the equation. -41.375 + 41.375 + x = 6.625 + 41.375 Combine like terms: -41.375 + 41.375 = 0.000 0.000 + x = 6.625 + 41.375 x = 6.625 + 41.375 Combine like terms: 6.625 + 41.375 = 48 x = 48 Simplifying x = 48Subproblem 2
x + -41.375 = -6.625 Simplifying x + -41.375 = -6.625 Reorder the terms: -41.375 + x = -6.625 Solving -41.375 + x = -6.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '41.375' to each side of the equation. -41.375 + 41.375 + x = -6.625 + 41.375 Combine like terms: -41.375 + 41.375 = 0.000 0.000 + x = -6.625 + 41.375 x = -6.625 + 41.375 Combine like terms: -6.625 + 41.375 = 34.75 x = 34.75 Simplifying x = 34.75Solution
The solution to the problem is based on the solutions from the subproblems. x = {48, 34.75}
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