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Simplifying
(7x + 8y)(7x + -8y) = 0
Multiply (7x + 8y) * (7x + -8y)
(7x * (7x + -8y) + 8y * (7x + -8y)) = 0
((7x * 7x + -8y * 7x) + 8y * (7x + -8y)) = 0
Reorder the terms:
((-56xy + 49x2) + 8y * (7x + -8y)) = 0
((-56xy + 49x2) + 8y * (7x + -8y)) = 0
(-56xy + 49x2 + (7x * 8y + -8y * 8y)) = 0
(-56xy + 49x2 + (56xy + -64y2)) = 0
Reorder the terms:
(-56xy + 56xy + 49x2 + -64y2) = 0
Combine like terms: -56xy + 56xy = 0
(0 + 49x2 + -64y2) = 0
(49x2 + -64y2) = 0
Solving
49x2 + -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.
49x2 + -64y2 + 64y2 = 0 + 64y2
Combine like terms: -64y2 + 64y2 = 0
49x2 + 0 = 0 + 64y2
49x2 = 0 + 64y2
Remove the zero:
49x2 = 64y2
Divide each side by '49'.
x2 = 1.306122449y2
Simplifying
x2 = 1.306122449y2
Take the square root of each side:
x = {-1.142857143y, 1.142857143y}
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