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Simplifying (4x + 17)(5x + 5) = 132 Reorder the terms: (17 + 4x)(5x + 5) = 132 Reorder the terms: (17 + 4x)(5 + 5x) = 132 Multiply (17 + 4x) * (5 + 5x) (17(5 + 5x) + 4x * (5 + 5x)) = 132 ((5 * 17 + 5x * 17) + 4x * (5 + 5x)) = 132 ((85 + 85x) + 4x * (5 + 5x)) = 132 (85 + 85x + (5 * 4x + 5x * 4x)) = 132 (85 + 85x + (20x + 20x2)) = 132 Combine like terms: 85x + 20x = 105x (85 + 105x + 20x2) = 132 Solving 85 + 105x + 20x2 = 132 Solving for variable 'x'. Reorder the terms: 85 + -132 + 105x + 20x2 = 132 + -132 Combine like terms: 85 + -132 = -47 -47 + 105x + 20x2 = 132 + -132 Combine like terms: 132 + -132 = 0 -47 + 105x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -2.35 + 5.25x + x2 = 0.0 Move the constant term to the right: Add '2.35' to each side of the equation. -2.35 + 5.25x + 2.35 + x2 = 0.0 + 2.35 Reorder the terms: -2.35 + 2.35 + 5.25x + x2 = 0.0 + 2.35 Combine like terms: -2.35 + 2.35 = 0.00 0.00 + 5.25x + x2 = 0.0 + 2.35 5.25x + x2 = 0.0 + 2.35 Combine like terms: 0.0 + 2.35 = 2.35 5.25x + x2 = 2.35 The x term is 5.25x. Take half its coefficient (2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. 5.25x + 6.890625 + x2 = 2.35 + 6.890625 Reorder the terms: 6.890625 + 5.25x + x2 = 2.35 + 6.890625 Combine like terms: 2.35 + 6.890625 = 9.240625 6.890625 + 5.25x + x2 = 9.240625 Factor a perfect square on the left side: (x + 2.625)(x + 2.625) = 9.240625 Calculate the square root of the right side: 3.039839634 Break this problem into two subproblems by setting (x + 2.625) equal to 3.039839634 and -3.039839634.Subproblem 1
x + 2.625 = 3.039839634 Simplifying x + 2.625 = 3.039839634 Reorder the terms: 2.625 + x = 3.039839634 Solving 2.625 + x = 3.039839634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = 3.039839634 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = 3.039839634 + -2.625 x = 3.039839634 + -2.625 Combine like terms: 3.039839634 + -2.625 = 0.414839634 x = 0.414839634 Simplifying x = 0.414839634Subproblem 2
x + 2.625 = -3.039839634 Simplifying x + 2.625 = -3.039839634 Reorder the terms: 2.625 + x = -3.039839634 Solving 2.625 + x = -3.039839634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = -3.039839634 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = -3.039839634 + -2.625 x = -3.039839634 + -2.625 Combine like terms: -3.039839634 + -2.625 = -5.664839634 x = -5.664839634 Simplifying x = -5.664839634Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.414839634, -5.664839634}
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