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Simplifying
(4x + -5y)(4x + 5y) = 0
Multiply (4x + -5y) * (4x + 5y)
(4x * (4x + 5y) + -5y * (4x + 5y)) = 0
((4x * 4x + 5y * 4x) + -5y * (4x + 5y)) = 0
Reorder the terms:
((20xy + 16x2) + -5y * (4x + 5y)) = 0
((20xy + 16x2) + -5y * (4x + 5y)) = 0
(20xy + 16x2 + (4x * -5y + 5y * -5y)) = 0
(20xy + 16x2 + (-20xy + -25y2)) = 0
Reorder the terms:
(20xy + -20xy + 16x2 + -25y2) = 0
Combine like terms: 20xy + -20xy = 0
(0 + 16x2 + -25y2) = 0
(16x2 + -25y2) = 0
Solving
16x2 + -25y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '25y2' to each side of the equation.
16x2 + -25y2 + 25y2 = 0 + 25y2
Combine like terms: -25y2 + 25y2 = 0
16x2 + 0 = 0 + 25y2
16x2 = 0 + 25y2
Remove the zero:
16x2 = 25y2
Divide each side by '16'.
x2 = 1.5625y2
Simplifying
x2 = 1.5625y2
Take the square root of each side:
x = {-1.25y, 1.25y}
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