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Simplifying
(10x + 8y)(10x + -8y) = 0
Multiply (10x + 8y) * (10x + -8y)
(10x * (10x + -8y) + 8y * (10x + -8y)) = 0
((10x * 10x + -8y * 10x) + 8y * (10x + -8y)) = 0
Reorder the terms:
((-80xy + 100x2) + 8y * (10x + -8y)) = 0
((-80xy + 100x2) + 8y * (10x + -8y)) = 0
(-80xy + 100x2 + (10x * 8y + -8y * 8y)) = 0
(-80xy + 100x2 + (80xy + -64y2)) = 0
Reorder the terms:
(-80xy + 80xy + 100x2 + -64y2) = 0
Combine like terms: -80xy + 80xy = 0
(0 + 100x2 + -64y2) = 0
(100x2 + -64y2) = 0
Solving
100x2 + -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.
100x2 + -64y2 + 64y2 = 0 + 64y2
Combine like terms: -64y2 + 64y2 = 0
100x2 + 0 = 0 + 64y2
100x2 = 0 + 64y2
Remove the zero:
100x2 = 64y2
Divide each side by '100'.
x2 = 0.64y2
Simplifying
x2 = 0.64y2
Take the square root of each side:
x = {-0.8y, 0.8y}
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