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Simplifying (5x + -1y)(5x + y) = 0 Multiply (5x + -1y) * (5x + y) (5x * (5x + y) + -1y * (5x + y)) = 0 ((5x * 5x + y * 5x) + -1y * (5x + y)) = 0 Reorder the terms: ((5xy + 25x2) + -1y * (5x + y)) = 0 ((5xy + 25x2) + -1y * (5x + y)) = 0 (5xy + 25x2 + (5x * -1y + y * -1y)) = 0 (5xy + 25x2 + (-5xy + -1y2)) = 0 Reorder the terms: (5xy + -5xy + 25x2 + -1y2) = 0 Combine like terms: 5xy + -5xy = 0 (0 + 25x2 + -1y2) = 0 (25x2 + -1y2) = 0 Solving 25x2 + -1y2 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add 'y2' to each side of the equation. 25x2 + -1y2 + y2 = 0 + y2 Combine like terms: -1y2 + y2 = 0 25x2 + 0 = 0 + y2 25x2 = 0 + y2 Remove the zero: 25x2 = y2 Divide each side by '25'. x2 = 0.04y2 Simplifying x2 = 0.04y2 Take the square root of each side: x = {-0.2y, 0.2y}
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