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Simplifying
(5x + -6y)(5x + 6y) = 0
Multiply (5x + -6y) * (5x + 6y)
(5x * (5x + 6y) + -6y * (5x + 6y)) = 0
((5x * 5x + 6y * 5x) + -6y * (5x + 6y)) = 0
Reorder the terms:
((30xy + 25x2) + -6y * (5x + 6y)) = 0
((30xy + 25x2) + -6y * (5x + 6y)) = 0
(30xy + 25x2 + (5x * -6y + 6y * -6y)) = 0
(30xy + 25x2 + (-30xy + -36y2)) = 0
Reorder the terms:
(30xy + -30xy + 25x2 + -36y2) = 0
Combine like terms: 30xy + -30xy = 0
(0 + 25x2 + -36y2) = 0
(25x2 + -36y2) = 0
Solving
25x2 + -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.
25x2 + -36y2 + 36y2 = 0 + 36y2
Combine like terms: -36y2 + 36y2 = 0
25x2 + 0 = 0 + 36y2
25x2 = 0 + 36y2
Remove the zero:
25x2 = 36y2
Divide each side by '25'.
x2 = 1.44y2
Simplifying
x2 = 1.44y2
Take the square root of each side:
x = {-1.2y, 1.2y}
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