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Simplifying
(15x + -16y)(15x + 16y) = 0
Multiply (15x + -16y) * (15x + 16y)
(15x * (15x + 16y) + -16y * (15x + 16y)) = 0
((15x * 15x + 16y * 15x) + -16y * (15x + 16y)) = 0
Reorder the terms:
((240xy + 225x2) + -16y * (15x + 16y)) = 0
((240xy + 225x2) + -16y * (15x + 16y)) = 0
(240xy + 225x2 + (15x * -16y + 16y * -16y)) = 0
(240xy + 225x2 + (-240xy + -256y2)) = 0
Reorder the terms:
(240xy + -240xy + 225x2 + -256y2) = 0
Combine like terms: 240xy + -240xy = 0
(0 + 225x2 + -256y2) = 0
(225x2 + -256y2) = 0
Solving
225x2 + -256y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '256y2' to each side of the equation.
225x2 + -256y2 + 256y2 = 0 + 256y2
Combine like terms: -256y2 + 256y2 = 0
225x2 + 0 = 0 + 256y2
225x2 = 0 + 256y2
Remove the zero:
225x2 = 256y2
Divide each side by '225'.
x2 = 1.137777778y2
Simplifying
x2 = 1.137777778y2
Take the square root of each side:
x = {-1.066666667y, 1.066666667y}
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