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Simplifying (4x2 + 2xy) + (2xy + y2) = 0 Reorder the terms: (2xy + 4x2) + (2xy + y2) = 0 Remove parenthesis around (2xy + 4x2) 2xy + 4x2 + (2xy + y2) = 0 Remove parenthesis around (2xy + y2) 2xy + 4x2 + 2xy + y2 = 0 Reorder the terms: 2xy + 2xy + 4x2 + y2 = 0 Combine like terms: 2xy + 2xy = 4xy 4xy + 4x2 + y2 = 0 Solving 4xy + 4x2 + y2 = 0 Solving for variable 'x'. Factor a trinomial. (2x + y)(2x + y) = 0Subproblem 1
Set the factor '(2x + y)' equal to zero and attempt to solve: Simplifying 2x + y = 0 Solving 2x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 2x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 2x + 0 = 0 + -1y 2x = 0 + -1y Remove the zero: 2x = -1y Divide each side by '2'. x = -0.5y Simplifying x = -0.5ySubproblem 2
Set the factor '(2x + y)' equal to zero and attempt to solve: Simplifying 2x + y = 0 Solving 2x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 2x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 2x + 0 = 0 + -1y 2x = 0 + -1y Remove the zero: 2x = -1y Divide each side by '2'. x = -0.5y Simplifying x = -0.5ySolution
x = {-0.5y, -0.5y}
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