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Simplifying
(5x + y)(5x + -1y) = 0
Multiply (5x + y) * (5x + -1y)
(5x * (5x + -1y) + y(5x + -1y)) = 0
((5x * 5x + -1y * 5x) + y(5x + -1y)) = 0
Reorder the terms:
((-5xy + 25x2) + y(5x + -1y)) = 0
((-5xy + 25x2) + y(5x + -1y)) = 0
(-5xy + 25x2 + (5x * y + -1y * y)) = 0
(-5xy + 25x2 + (5xy + -1y2)) = 0
Reorder the terms:
(-5xy + 5xy + 25x2 + -1y2) = 0
Combine like terms: -5xy + 5xy = 0
(0 + 25x2 + -1y2) = 0
(25x2 + -1y2) = 0
Solving
25x2 + -1y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add 'y2' to each side of the equation.
25x2 + -1y2 + y2 = 0 + y2
Combine like terms: -1y2 + y2 = 0
25x2 + 0 = 0 + y2
25x2 = 0 + y2
Remove the zero:
25x2 = y2
Divide each side by '25'.
x2 = 0.04y2
Simplifying
x2 = 0.04y2
Take the square root of each side:
x = {-0.2y, 0.2y}
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