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Simplifying
(5x + -2y)(5x + 2y) = 0
Multiply (5x + -2y) * (5x + 2y)
(5x * (5x + 2y) + -2y * (5x + 2y)) = 0
((5x * 5x + 2y * 5x) + -2y * (5x + 2y)) = 0
Reorder the terms:
((10xy + 25x2) + -2y * (5x + 2y)) = 0
((10xy + 25x2) + -2y * (5x + 2y)) = 0
(10xy + 25x2 + (5x * -2y + 2y * -2y)) = 0
(10xy + 25x2 + (-10xy + -4y2)) = 0
Reorder the terms:
(10xy + -10xy + 25x2 + -4y2) = 0
Combine like terms: 10xy + -10xy = 0
(0 + 25x2 + -4y2) = 0
(25x2 + -4y2) = 0
Solving
25x2 + -4y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '4y2' to each side of the equation.
25x2 + -4y2 + 4y2 = 0 + 4y2
Combine like terms: -4y2 + 4y2 = 0
25x2 + 0 = 0 + 4y2
25x2 = 0 + 4y2
Remove the zero:
25x2 = 4y2
Divide each side by '25'.
x2 = 0.16y2
Simplifying
x2 = 0.16y2
Take the square root of each side:
x = {-0.4y, 0.4y}
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