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Simplifying (5x + -1y)(2x + y) = 0 Multiply (5x + -1y) * (2x + y) (5x * (2x + y) + -1y * (2x + y)) = 0 ((2x * 5x + y * 5x) + -1y * (2x + y)) = 0 Reorder the terms: ((5xy + 10x2) + -1y * (2x + y)) = 0 ((5xy + 10x2) + -1y * (2x + y)) = 0 (5xy + 10x2 + (2x * -1y + y * -1y)) = 0 (5xy + 10x2 + (-2xy + -1y2)) = 0 Reorder the terms: (5xy + -2xy + 10x2 + -1y2) = 0 Combine like terms: 5xy + -2xy = 3xy (3xy + 10x2 + -1y2) = 0 Solving 3xy + 10x2 + -1y2 = 0 Solving for variable 'x'. Factor a trinomial. (5x + -1y)(2x + y) = 0Subproblem 1
Set the factor '(5x + -1y)' equal to zero and attempt to solve: Simplifying 5x + -1y = 0 Solving 5x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 5x + -1y + y = 0 + y Combine like terms: -1y + y = 0 5x + 0 = 0 + y 5x = 0 + y Remove the zero: 5x = y Divide each side by '5'. x = 0.2y Simplifying x = 0.2ySubproblem 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 = {0.2y, -0.5y}
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