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Simplifying
(7x + 5y)(7x + -5y) = 0
Multiply (7x + 5y) * (7x + -5y)
(7x * (7x + -5y) + 5y * (7x + -5y)) = 0
((7x * 7x + -5y * 7x) + 5y * (7x + -5y)) = 0
Reorder the terms:
((-35xy + 49x2) + 5y * (7x + -5y)) = 0
((-35xy + 49x2) + 5y * (7x + -5y)) = 0
(-35xy + 49x2 + (7x * 5y + -5y * 5y)) = 0
(-35xy + 49x2 + (35xy + -25y2)) = 0
Reorder the terms:
(-35xy + 35xy + 49x2 + -25y2) = 0
Combine like terms: -35xy + 35xy = 0
(0 + 49x2 + -25y2) = 0
(49x2 + -25y2) = 0
Solving
49x2 + -25y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '25y2' to each side of the equation.
49x2 + -25y2 + 25y2 = 0 + 25y2
Combine like terms: -25y2 + 25y2 = 0
49x2 + 0 = 0 + 25y2
49x2 = 0 + 25y2
Remove the zero:
49x2 = 25y2
Divide each side by '49'.
x2 = 0.5102040816y2
Simplifying
x2 = 0.5102040816y2
Take the square root of each side:
x = {-0.714285714y, 0.714285714y}
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