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Simplifying
(5x + -8y)(5x + 8y) = 0
Multiply (5x + -8y) * (5x + 8y)
(5x * (5x + 8y) + -8y * (5x + 8y)) = 0
((5x * 5x + 8y * 5x) + -8y * (5x + 8y)) = 0
Reorder the terms:
((40xy + 25x2) + -8y * (5x + 8y)) = 0
((40xy + 25x2) + -8y * (5x + 8y)) = 0
(40xy + 25x2 + (5x * -8y + 8y * -8y)) = 0
(40xy + 25x2 + (-40xy + -64y2)) = 0
Reorder the terms:
(40xy + -40xy + 25x2 + -64y2) = 0
Combine like terms: 40xy + -40xy = 0
(0 + 25x2 + -64y2) = 0
(25x2 + -64y2) = 0
Solving
25x2 + -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.
25x2 + -64y2 + 64y2 = 0 + 64y2
Combine like terms: -64y2 + 64y2 = 0
25x2 + 0 = 0 + 64y2
25x2 = 0 + 64y2
Remove the zero:
25x2 = 64y2
Divide each side by '25'.
x2 = 2.56y2
Simplifying
x2 = 2.56y2
Take the square root of each side:
x = {-1.6y, 1.6y}
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