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Simplifying (w + 500)(w + 130) = 3125 Reorder the terms: (500 + w)(w + 130) = 3125 Reorder the terms: (500 + w)(130 + w) = 3125 Multiply (500 + w) * (130 + w) (500(130 + w) + w(130 + w)) = 3125 ((130 * 500 + w * 500) + w(130 + w)) = 3125 ((65000 + 500w) + w(130 + w)) = 3125 (65000 + 500w + (130 * w + w * w)) = 3125 (65000 + 500w + (130w + w2)) = 3125 Combine like terms: 500w + 130w = 630w (65000 + 630w + w2) = 3125 Solving 65000 + 630w + w2 = 3125 Solving for variable 'w'. Reorder the terms: 65000 + -3125 + 630w + w2 = 3125 + -3125 Combine like terms: 65000 + -3125 = 61875 61875 + 630w + w2 = 3125 + -3125 Combine like terms: 3125 + -3125 = 0 61875 + 630w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-61875' to each side of the equation. 61875 + 630w + -61875 + w2 = 0 + -61875 Reorder the terms: 61875 + -61875 + 630w + w2 = 0 + -61875 Combine like terms: 61875 + -61875 = 0 0 + 630w + w2 = 0 + -61875 630w + w2 = 0 + -61875 Combine like terms: 0 + -61875 = -61875 630w + w2 = -61875 The w term is 630w. Take half its coefficient (315). Square it (99225) and add it to both sides. Add '99225' to each side of the equation. 630w + 99225 + w2 = -61875 + 99225 Reorder the terms: 99225 + 630w + w2 = -61875 + 99225 Combine like terms: -61875 + 99225 = 37350 99225 + 630w + w2 = 37350 Factor a perfect square on the left side: (w + 315)(w + 315) = 37350 Calculate the square root of the right side: 193.261480901 Break this problem into two subproblems by setting (w + 315) equal to 193.261480901 and -193.261480901.Subproblem 1
w + 315 = 193.261480901 Simplifying w + 315 = 193.261480901 Reorder the terms: 315 + w = 193.261480901 Solving 315 + w = 193.261480901 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-315' to each side of the equation. 315 + -315 + w = 193.261480901 + -315 Combine like terms: 315 + -315 = 0 0 + w = 193.261480901 + -315 w = 193.261480901 + -315 Combine like terms: 193.261480901 + -315 = -121.738519099 w = -121.738519099 Simplifying w = -121.738519099Subproblem 2
w + 315 = -193.261480901 Simplifying w + 315 = -193.261480901 Reorder the terms: 315 + w = -193.261480901 Solving 315 + w = -193.261480901 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-315' to each side of the equation. 315 + -315 + w = -193.261480901 + -315 Combine like terms: 315 + -315 = 0 0 + w = -193.261480901 + -315 w = -193.261480901 + -315 Combine like terms: -193.261480901 + -315 = -508.261480901 w = -508.261480901 Simplifying w = -508.261480901Solution
The solution to the problem is based on the solutions from the subproblems. w = {-121.738519099, -508.261480901}
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