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Simplifying
(5x + 9y)(5x + -9y) = 0
Multiply (5x + 9y) * (5x + -9y)
(5x * (5x + -9y) + 9y * (5x + -9y)) = 0
((5x * 5x + -9y * 5x) + 9y * (5x + -9y)) = 0
Reorder the terms:
((-45xy + 25x2) + 9y * (5x + -9y)) = 0
((-45xy + 25x2) + 9y * (5x + -9y)) = 0
(-45xy + 25x2 + (5x * 9y + -9y * 9y)) = 0
(-45xy + 25x2 + (45xy + -81y2)) = 0
Reorder the terms:
(-45xy + 45xy + 25x2 + -81y2) = 0
Combine like terms: -45xy + 45xy = 0
(0 + 25x2 + -81y2) = 0
(25x2 + -81y2) = 0
Solving
25x2 + -81y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '81y2' to each side of the equation.
25x2 + -81y2 + 81y2 = 0 + 81y2
Combine like terms: -81y2 + 81y2 = 0
25x2 + 0 = 0 + 81y2
25x2 = 0 + 81y2
Remove the zero:
25x2 = 81y2
Divide each side by '25'.
x2 = 3.24y2
Simplifying
x2 = 3.24y2
Take the square root of each side:
x = {-1.8y, 1.8y}
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