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Simplifying
(7x + -6y)(7x + 6y) = 0
Multiply (7x + -6y) * (7x + 6y)
(7x * (7x + 6y) + -6y * (7x + 6y)) = 0
((7x * 7x + 6y * 7x) + -6y * (7x + 6y)) = 0
Reorder the terms:
((42xy + 49x2) + -6y * (7x + 6y)) = 0
((42xy + 49x2) + -6y * (7x + 6y)) = 0
(42xy + 49x2 + (7x * -6y + 6y * -6y)) = 0
(42xy + 49x2 + (-42xy + -36y2)) = 0
Reorder the terms:
(42xy + -42xy + 49x2 + -36y2) = 0
Combine like terms: 42xy + -42xy = 0
(0 + 49x2 + -36y2) = 0
(49x2 + -36y2) = 0
Solving
49x2 + -36y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '36y2' to each side of the equation.
49x2 + -36y2 + 36y2 = 0 + 36y2
Combine like terms: -36y2 + 36y2 = 0
49x2 + 0 = 0 + 36y2
49x2 = 0 + 36y2
Remove the zero:
49x2 = 36y2
Divide each side by '49'.
x2 = 0.7346938776y2
Simplifying
x2 = 0.7346938776y2
Take the square root of each side:
x = {-0.857142857y, 0.857142857y}
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