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Simplifying
(9x + 8y)(9x + -8y) = 0
Multiply (9x + 8y) * (9x + -8y)
(9x * (9x + -8y) + 8y * (9x + -8y)) = 0
((9x * 9x + -8y * 9x) + 8y * (9x + -8y)) = 0
Reorder the terms:
((-72xy + 81x2) + 8y * (9x + -8y)) = 0
((-72xy + 81x2) + 8y * (9x + -8y)) = 0
(-72xy + 81x2 + (9x * 8y + -8y * 8y)) = 0
(-72xy + 81x2 + (72xy + -64y2)) = 0
Reorder the terms:
(-72xy + 72xy + 81x2 + -64y2) = 0
Combine like terms: -72xy + 72xy = 0
(0 + 81x2 + -64y2) = 0
(81x2 + -64y2) = 0
Solving
81x2 + -64y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '64y2' to each side of the equation.
81x2 + -64y2 + 64y2 = 0 + 64y2
Combine like terms: -64y2 + 64y2 = 0
81x2 + 0 = 0 + 64y2
81x2 = 0 + 64y2
Remove the zero:
81x2 = 64y2
Divide each side by '81'.
x2 = 0.7901234568y2
Simplifying
x2 = 0.7901234568y2
Take the square root of each side:
x = {-0.888888889y, 0.888888889y}
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