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Simplifying
(9x + 4y)(9x + -4y) = 0
Multiply (9x + 4y) * (9x + -4y)
(9x * (9x + -4y) + 4y * (9x + -4y)) = 0
((9x * 9x + -4y * 9x) + 4y * (9x + -4y)) = 0
Reorder the terms:
((-36xy + 81x2) + 4y * (9x + -4y)) = 0
((-36xy + 81x2) + 4y * (9x + -4y)) = 0
(-36xy + 81x2 + (9x * 4y + -4y * 4y)) = 0
(-36xy + 81x2 + (36xy + -16y2)) = 0
Reorder the terms:
(-36xy + 36xy + 81x2 + -16y2) = 0
Combine like terms: -36xy + 36xy = 0
(0 + 81x2 + -16y2) = 0
(81x2 + -16y2) = 0
Solving
81x2 + -16y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '16y2' to each side of the equation.
81x2 + -16y2 + 16y2 = 0 + 16y2
Combine like terms: -16y2 + 16y2 = 0
81x2 + 0 = 0 + 16y2
81x2 = 0 + 16y2
Remove the zero:
81x2 = 16y2
Divide each side by '81'.
x2 = 0.1975308642y2
Simplifying
x2 = 0.1975308642y2
Take the square root of each side:
x = {-0.444444444y, 0.444444444y}
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