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Simplifying
(9x + -7y)(9x + 7y) = 0
Multiply (9x + -7y) * (9x + 7y)
(9x * (9x + 7y) + -7y * (9x + 7y)) = 0
((9x * 9x + 7y * 9x) + -7y * (9x + 7y)) = 0
Reorder the terms:
((63xy + 81x2) + -7y * (9x + 7y)) = 0
((63xy + 81x2) + -7y * (9x + 7y)) = 0
(63xy + 81x2 + (9x * -7y + 7y * -7y)) = 0
(63xy + 81x2 + (-63xy + -49y2)) = 0
Reorder the terms:
(63xy + -63xy + 81x2 + -49y2) = 0
Combine like terms: 63xy + -63xy = 0
(0 + 81x2 + -49y2) = 0
(81x2 + -49y2) = 0
Solving
81x2 + -49y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '49y2' to each side of the equation.
81x2 + -49y2 + 49y2 = 0 + 49y2
Combine like terms: -49y2 + 49y2 = 0
81x2 + 0 = 0 + 49y2
81x2 = 0 + 49y2
Remove the zero:
81x2 = 49y2
Divide each side by '81'.
x2 = 0.6049382716y2
Simplifying
x2 = 0.6049382716y2
Take the square root of each side:
x = {-0.777777778y, 0.777777778y}
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