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Simplifying (4x + 2y)(2x + y) = 100 Multiply (4x + 2y) * (2x + y) (4x * (2x + y) + 2y * (2x + y)) = 100 ((2x * 4x + y * 4x) + 2y * (2x + y)) = 100 Reorder the terms: ((4xy + 8x2) + 2y * (2x + y)) = 100 ((4xy + 8x2) + 2y * (2x + y)) = 100 (4xy + 8x2 + (2x * 2y + y * 2y)) = 100 (4xy + 8x2 + (4xy + 2y2)) = 100 Reorder the terms: (4xy + 4xy + 8x2 + 2y2) = 100 Combine like terms: 4xy + 4xy = 8xy (8xy + 8x2 + 2y2) = 100 Solving 8xy + 8x2 + 2y2 = 100 Solving for variable 'x'. Reorder the terms: -100 + 8xy + 8x2 + 2y2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 8xy + 8x2 + 2y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-50 + 4xy + 4x2 + y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-50 + 4xy + 4x2 + y2)' equal to zero and attempt to solve: Simplifying -50 + 4xy + 4x2 + y2 = 0 Solving -50 + 4xy + 4x2 + y2 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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