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Simplifying (9x + 5y)(9x + -5y) = 0 Multiply (9x + 5y) * (9x + -5y) (9x * (9x + -5y) + 5y * (9x + -5y)) = 0 ((9x * 9x + -5y * 9x) + 5y * (9x + -5y)) = 0 Reorder the terms: ((-45xy + 81x2) + 5y * (9x + -5y)) = 0 ((-45xy + 81x2) + 5y * (9x + -5y)) = 0 (-45xy + 81x2 + (9x * 5y + -5y * 5y)) = 0 (-45xy + 81x2 + (45xy + -25y2)) = 0 Reorder the terms: (-45xy + 45xy + 81x2 + -25y2) = 0 Combine like terms: -45xy + 45xy = 0 (0 + 81x2 + -25y2) = 0 (81x2 + -25y2) = 0 Solving 81x2 + -25y2 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25y2' to each side of the equation. 81x2 + -25y2 + 25y2 = 0 + 25y2 Combine like terms: -25y2 + 25y2 = 0 81x2 + 0 = 0 + 25y2 81x2 = 0 + 25y2 Remove the zero: 81x2 = 25y2 Divide each side by '81'. x2 = 0.3086419753y2 Simplifying x2 = 0.3086419753y2 Take the square root of each side: x = {-0.555555556y, 0.555555556y}
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