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Simplifying (5x + -1y)(5x + -1y) = 0 Multiply (5x + -1y) * (5x + -1y) (5x * (5x + -1y) + -1y * (5x + -1y)) = 0 ((5x * 5x + -1y * 5x) + -1y * (5x + -1y)) = 0 Reorder the terms: ((-5xy + 25x2) + -1y * (5x + -1y)) = 0 ((-5xy + 25x2) + -1y * (5x + -1y)) = 0 (-5xy + 25x2 + (5x * -1y + -1y * -1y)) = 0 (-5xy + 25x2 + (-5xy + 1y2)) = 0 Reorder the terms: (-5xy + -5xy + 25x2 + 1y2) = 0 Combine like terms: -5xy + -5xy = -10xy (-10xy + 25x2 + 1y2) = 0 Solving -10xy + 25x2 + 1y2 = 0 Solving for variable 'x'. Factor a trinomial. (5x + -1y)(5x + -1y) = 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 '(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 = 0.2ySolution
x = {0.2y, 0.2y}
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