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Simplifying (x + 375)(x + 240) = x Reorder the terms: (375 + x)(x + 240) = x Reorder the terms: (375 + x)(240 + x) = x Multiply (375 + x) * (240 + x) (375(240 + x) + x(240 + x)) = x ((240 * 375 + x * 375) + x(240 + x)) = x ((90000 + 375x) + x(240 + x)) = x (90000 + 375x + (240 * x + x * x)) = x (90000 + 375x + (240x + x2)) = x Combine like terms: 375x + 240x = 615x (90000 + 615x + x2) = x Solving 90000 + 615x + x2 = x Solving for variable 'x'. Reorder the terms: 90000 + 615x + -1x + x2 = x + -1x Combine like terms: 615x + -1x = 614x 90000 + 614x + x2 = x + -1x Combine like terms: x + -1x = 0 90000 + 614x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-90000' to each side of the equation. 90000 + 614x + -90000 + x2 = 0 + -90000 Reorder the terms: 90000 + -90000 + 614x + x2 = 0 + -90000 Combine like terms: 90000 + -90000 = 0 0 + 614x + x2 = 0 + -90000 614x + x2 = 0 + -90000 Combine like terms: 0 + -90000 = -90000 614x + x2 = -90000 The x term is 614x. Take half its coefficient (307). Square it (94249) and add it to both sides. Add '94249' to each side of the equation. 614x + 94249 + x2 = -90000 + 94249 Reorder the terms: 94249 + 614x + x2 = -90000 + 94249 Combine like terms: -90000 + 94249 = 4249 94249 + 614x + x2 = 4249 Factor a perfect square on the left side: (x + 307)(x + 307) = 4249 Calculate the square root of the right side: 65.184353951 Break this problem into two subproblems by setting (x + 307) equal to 65.184353951 and -65.184353951.Subproblem 1
x + 307 = 65.184353951 Simplifying x + 307 = 65.184353951 Reorder the terms: 307 + x = 65.184353951 Solving 307 + x = 65.184353951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-307' to each side of the equation. 307 + -307 + x = 65.184353951 + -307 Combine like terms: 307 + -307 = 0 0 + x = 65.184353951 + -307 x = 65.184353951 + -307 Combine like terms: 65.184353951 + -307 = -241.815646049 x = -241.815646049 Simplifying x = -241.815646049Subproblem 2
x + 307 = -65.184353951 Simplifying x + 307 = -65.184353951 Reorder the terms: 307 + x = -65.184353951 Solving 307 + x = -65.184353951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-307' to each side of the equation. 307 + -307 + x = -65.184353951 + -307 Combine like terms: 307 + -307 = 0 0 + x = -65.184353951 + -307 x = -65.184353951 + -307 Combine like terms: -65.184353951 + -307 = -372.184353951 x = -372.184353951 Simplifying x = -372.184353951Solution
The solution to the problem is based on the solutions from the subproblems. x = {-241.815646049, -372.184353951}
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