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Simplifying (2x + -1y)(x + 5y) = 0 Multiply (2x + -1y) * (x + 5y) (2x * (x + 5y) + -1y * (x + 5y)) = 0 ((x * 2x + 5y * 2x) + -1y * (x + 5y)) = 0 Reorder the terms: ((10xy + 2x2) + -1y * (x + 5y)) = 0 ((10xy + 2x2) + -1y * (x + 5y)) = 0 (10xy + 2x2 + (x * -1y + 5y * -1y)) = 0 (10xy + 2x2 + (-1xy + -5y2)) = 0 Reorder the terms: (10xy + -1xy + 2x2 + -5y2) = 0 Combine like terms: 10xy + -1xy = 9xy (9xy + 2x2 + -5y2) = 0 Solving 9xy + 2x2 + -5y2 = 0 Solving for variable 'x'. Factor a trinomial. (2x + -1y)(x + 5y) = 0Subproblem 1
Set the factor '(2x + -1y)' equal to zero and attempt to solve: Simplifying 2x + -1y = 0 Solving 2x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 2x + -1y + y = 0 + y Combine like terms: -1y + y = 0 2x + 0 = 0 + y 2x = 0 + y Remove the zero: 2x = y Divide each side by '2'. x = 0.5y Simplifying x = 0.5ySubproblem 2
Set the factor '(x + 5y)' equal to zero and attempt to solve: Simplifying x + 5y = 0 Solving x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 x + 0 = 0 + -5y x = 0 + -5y Remove the zero: x = -5y Simplifying x = -5ySolution
x = {0.5y, -5y}
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