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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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