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Simplifying
(4x + -9y)(4x + 9y) = 0
Multiply (4x + -9y) * (4x + 9y)
(4x * (4x + 9y) + -9y * (4x + 9y)) = 0
((4x * 4x + 9y * 4x) + -9y * (4x + 9y)) = 0
Reorder the terms:
((36xy + 16x2) + -9y * (4x + 9y)) = 0
((36xy + 16x2) + -9y * (4x + 9y)) = 0
(36xy + 16x2 + (4x * -9y + 9y * -9y)) = 0
(36xy + 16x2 + (-36xy + -81y2)) = 0
Reorder the terms:
(36xy + -36xy + 16x2 + -81y2) = 0
Combine like terms: 36xy + -36xy = 0
(0 + 16x2 + -81y2) = 0
(16x2 + -81y2) = 0
Solving
16x2 + -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.
16x2 + -81y2 + 81y2 = 0 + 81y2
Combine like terms: -81y2 + 81y2 = 0
16x2 + 0 = 0 + 81y2
16x2 = 0 + 81y2
Remove the zero:
16x2 = 81y2
Divide each side by '16'.
x2 = 5.0625y2
Simplifying
x2 = 5.0625y2
Take the square root of each side:
x = {-2.25y, 2.25y}
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