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Simplifying
(7x + -3y)(7x + 3y) = 0
Multiply (7x + -3y) * (7x + 3y)
(7x * (7x + 3y) + -3y * (7x + 3y)) = 0
((7x * 7x + 3y * 7x) + -3y * (7x + 3y)) = 0
Reorder the terms:
((21xy + 49x2) + -3y * (7x + 3y)) = 0
((21xy + 49x2) + -3y * (7x + 3y)) = 0
(21xy + 49x2 + (7x * -3y + 3y * -3y)) = 0
(21xy + 49x2 + (-21xy + -9y2)) = 0
Reorder the terms:
(21xy + -21xy + 49x2 + -9y2) = 0
Combine like terms: 21xy + -21xy = 0
(0 + 49x2 + -9y2) = 0
(49x2 + -9y2) = 0
Solving
49x2 + -9y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '9y2' to each side of the equation.
49x2 + -9y2 + 9y2 = 0 + 9y2
Combine like terms: -9y2 + 9y2 = 0
49x2 + 0 = 0 + 9y2
49x2 = 0 + 9y2
Remove the zero:
49x2 = 9y2
Divide each side by '49'.
x2 = 0.1836734694y2
Simplifying
x2 = 0.1836734694y2
Take the square root of each side:
x = {-0.428571429y, 0.428571429y}
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