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Simplifying (240 + x)(375 + x) = 171000 Multiply (240 + x) * (375 + x) (240(375 + x) + x(375 + x)) = 171000 ((375 * 240 + x * 240) + x(375 + x)) = 171000 ((90000 + 240x) + x(375 + x)) = 171000 (90000 + 240x + (375 * x + x * x)) = 171000 (90000 + 240x + (375x + x2)) = 171000 Combine like terms: 240x + 375x = 615x (90000 + 615x + x2) = 171000 Solving 90000 + 615x + x2 = 171000 Solving for variable 'x'. Reorder the terms: 90000 + -171000 + 615x + x2 = 171000 + -171000 Combine like terms: 90000 + -171000 = -81000 -81000 + 615x + x2 = 171000 + -171000 Combine like terms: 171000 + -171000 = 0 -81000 + 615x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '81000' to each side of the equation. -81000 + 615x + 81000 + x2 = 0 + 81000 Reorder the terms: -81000 + 81000 + 615x + x2 = 0 + 81000 Combine like terms: -81000 + 81000 = 0 0 + 615x + x2 = 0 + 81000 615x + x2 = 0 + 81000 Combine like terms: 0 + 81000 = 81000 615x + x2 = 81000 The x term is 615x. Take half its coefficient (307.5). Square it (94556.25) and add it to both sides. Add '94556.25' to each side of the equation. 615x + 94556.25 + x2 = 81000 + 94556.25 Reorder the terms: 94556.25 + 615x + x2 = 81000 + 94556.25 Combine like terms: 81000 + 94556.25 = 175556.25 94556.25 + 615x + x2 = 175556.25 Factor a perfect square on the left side: (x + 307.5)(x + 307.5) = 175556.25 Calculate the square root of the right side: 418.994331704 Break this problem into two subproblems by setting (x + 307.5) equal to 418.994331704 and -418.994331704.Subproblem 1
x + 307.5 = 418.994331704 Simplifying x + 307.5 = 418.994331704 Reorder the terms: 307.5 + x = 418.994331704 Solving 307.5 + x = 418.994331704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-307.5' to each side of the equation. 307.5 + -307.5 + x = 418.994331704 + -307.5 Combine like terms: 307.5 + -307.5 = 0.0 0.0 + x = 418.994331704 + -307.5 x = 418.994331704 + -307.5 Combine like terms: 418.994331704 + -307.5 = 111.494331704 x = 111.494331704 Simplifying x = 111.494331704Subproblem 2
x + 307.5 = -418.994331704 Simplifying x + 307.5 = -418.994331704 Reorder the terms: 307.5 + x = -418.994331704 Solving 307.5 + x = -418.994331704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-307.5' to each side of the equation. 307.5 + -307.5 + x = -418.994331704 + -307.5 Combine like terms: 307.5 + -307.5 = 0.0 0.0 + x = -418.994331704 + -307.5 x = -418.994331704 + -307.5 Combine like terms: -418.994331704 + -307.5 = -726.494331704 x = -726.494331704 Simplifying x = -726.494331704Solution
The solution to the problem is based on the solutions from the subproblems. x = {111.494331704, -726.494331704}
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