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Simplifying
(3x + 8y)(3x + -8y) = 0
Multiply (3x + 8y) * (3x + -8y)
(3x * (3x + -8y) + 8y * (3x + -8y)) = 0
((3x * 3x + -8y * 3x) + 8y * (3x + -8y)) = 0
Reorder the terms:
((-24xy + 9x2) + 8y * (3x + -8y)) = 0
((-24xy + 9x2) + 8y * (3x + -8y)) = 0
(-24xy + 9x2 + (3x * 8y + -8y * 8y)) = 0
(-24xy + 9x2 + (24xy + -64y2)) = 0
Reorder the terms:
(-24xy + 24xy + 9x2 + -64y2) = 0
Combine like terms: -24xy + 24xy = 0
(0 + 9x2 + -64y2) = 0
(9x2 + -64y2) = 0
Solving
9x2 + -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.
9x2 + -64y2 + 64y2 = 0 + 64y2
Combine like terms: -64y2 + 64y2 = 0
9x2 + 0 = 0 + 64y2
9x2 = 0 + 64y2
Remove the zero:
9x2 = 64y2
Divide each side by '9'.
x2 = 7.111111111y2
Simplifying
x2 = 7.111111111y2
Take the square root of each side:
x = {-2.666666667y, 2.666666667y}
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