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Simplifying (x + 130)(x + 500) = 3125 Reorder the terms: (130 + x)(x + 500) = 3125 Reorder the terms: (130 + x)(500 + x) = 3125 Multiply (130 + x) * (500 + x) (130(500 + x) + x(500 + x)) = 3125 ((500 * 130 + x * 130) + x(500 + x)) = 3125 ((65000 + 130x) + x(500 + x)) = 3125 (65000 + 130x + (500 * x + x * x)) = 3125 (65000 + 130x + (500x + x2)) = 3125 Combine like terms: 130x + 500x = 630x (65000 + 630x + x2) = 3125 Solving 65000 + 630x + x2 = 3125 Solving for variable 'x'. Reorder the terms: 65000 + -3125 + 630x + x2 = 3125 + -3125 Combine like terms: 65000 + -3125 = 61875 61875 + 630x + x2 = 3125 + -3125 Combine like terms: 3125 + -3125 = 0 61875 + 630x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-61875' to each side of the equation. 61875 + 630x + -61875 + x2 = 0 + -61875 Reorder the terms: 61875 + -61875 + 630x + x2 = 0 + -61875 Combine like terms: 61875 + -61875 = 0 0 + 630x + x2 = 0 + -61875 630x + x2 = 0 + -61875 Combine like terms: 0 + -61875 = -61875 630x + x2 = -61875 The x term is 630x. Take half its coefficient (315). Square it (99225) and add it to both sides. Add '99225' to each side of the equation. 630x + 99225 + x2 = -61875 + 99225 Reorder the terms: 99225 + 630x + x2 = -61875 + 99225 Combine like terms: -61875 + 99225 = 37350 99225 + 630x + x2 = 37350 Factor a perfect square on the left side: (x + 315)(x + 315) = 37350 Calculate the square root of the right side: 193.261480901 Break this problem into two subproblems by setting (x + 315) equal to 193.261480901 and -193.261480901.Subproblem 1
x + 315 = 193.261480901 Simplifying x + 315 = 193.261480901 Reorder the terms: 315 + x = 193.261480901 Solving 315 + x = 193.261480901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-315' to each side of the equation. 315 + -315 + x = 193.261480901 + -315 Combine like terms: 315 + -315 = 0 0 + x = 193.261480901 + -315 x = 193.261480901 + -315 Combine like terms: 193.261480901 + -315 = -121.738519099 x = -121.738519099 Simplifying x = -121.738519099Subproblem 2
x + 315 = -193.261480901 Simplifying x + 315 = -193.261480901 Reorder the terms: 315 + x = -193.261480901 Solving 315 + x = -193.261480901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-315' to each side of the equation. 315 + -315 + x = -193.261480901 + -315 Combine like terms: 315 + -315 = 0 0 + x = -193.261480901 + -315 x = -193.261480901 + -315 Combine like terms: -193.261480901 + -315 = -508.261480901 x = -508.261480901 Simplifying x = -508.261480901Solution
The solution to the problem is based on the solutions from the subproblems. x = {-121.738519099, -508.261480901}
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