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Simplifying (360 + x)(159 + x) = 72000 Multiply (360 + x) * (159 + x) (360(159 + x) + x(159 + x)) = 72000 ((159 * 360 + x * 360) + x(159 + x)) = 72000 ((57240 + 360x) + x(159 + x)) = 72000 (57240 + 360x + (159 * x + x * x)) = 72000 (57240 + 360x + (159x + x2)) = 72000 Combine like terms: 360x + 159x = 519x (57240 + 519x + x2) = 72000 Solving 57240 + 519x + x2 = 72000 Solving for variable 'x'. Reorder the terms: 57240 + -72000 + 519x + x2 = 72000 + -72000 Combine like terms: 57240 + -72000 = -14760 -14760 + 519x + x2 = 72000 + -72000 Combine like terms: 72000 + -72000 = 0 -14760 + 519x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '14760' to each side of the equation. -14760 + 519x + 14760 + x2 = 0 + 14760 Reorder the terms: -14760 + 14760 + 519x + x2 = 0 + 14760 Combine like terms: -14760 + 14760 = 0 0 + 519x + x2 = 0 + 14760 519x + x2 = 0 + 14760 Combine like terms: 0 + 14760 = 14760 519x + x2 = 14760 The x term is 519x. Take half its coefficient (259.5). Square it (67340.25) and add it to both sides. Add '67340.25' to each side of the equation. 519x + 67340.25 + x2 = 14760 + 67340.25 Reorder the terms: 67340.25 + 519x + x2 = 14760 + 67340.25 Combine like terms: 14760 + 67340.25 = 82100.25 67340.25 + 519x + x2 = 82100.25 Factor a perfect square on the left side: (x + 259.5)(x + 259.5) = 82100.25 Calculate the square root of the right side: 286.531411891 Break this problem into two subproblems by setting (x + 259.5) equal to 286.531411891 and -286.531411891.Subproblem 1
x + 259.5 = 286.531411891 Simplifying x + 259.5 = 286.531411891 Reorder the terms: 259.5 + x = 286.531411891 Solving 259.5 + x = 286.531411891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-259.5' to each side of the equation. 259.5 + -259.5 + x = 286.531411891 + -259.5 Combine like terms: 259.5 + -259.5 = 0.0 0.0 + x = 286.531411891 + -259.5 x = 286.531411891 + -259.5 Combine like terms: 286.531411891 + -259.5 = 27.031411891 x = 27.031411891 Simplifying x = 27.031411891Subproblem 2
x + 259.5 = -286.531411891 Simplifying x + 259.5 = -286.531411891 Reorder the terms: 259.5 + x = -286.531411891 Solving 259.5 + x = -286.531411891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-259.5' to each side of the equation. 259.5 + -259.5 + x = -286.531411891 + -259.5 Combine like terms: 259.5 + -259.5 = 0.0 0.0 + x = -286.531411891 + -259.5 x = -286.531411891 + -259.5 Combine like terms: -286.531411891 + -259.5 = -546.031411891 x = -546.031411891 Simplifying x = -546.031411891Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.031411891, -546.031411891}
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