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Simplifying 5xy = 2x2 + 2y2 Solving 5xy = 2x2 + 2y2 Solving for variable 'x'. Reorder the terms: 5xy + -2x2 + -2y2 = 2x2 + -2x2 + 2y2 + -2y2 Combine like terms: 2x2 + -2x2 = 0 5xy + -2x2 + -2y2 = 0 + 2y2 + -2y2 5xy + -2x2 + -2y2 = 2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 5xy + -2x2 + -2y2 = 0 Factor a trinomial. (-2x + y)(x + -2y) = 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 '(x + -2y)' equal to zero and attempt to solve: Simplifying x + -2y = 0 Solving x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 x + 0 = 0 + 2y x = 0 + 2y Remove the zero: x = 2y Simplifying x = 2ySolution
x = {0.5y, 2y}
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