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Simplifying
(0.2x + -1y)(0.2x + y) = 0
Multiply (0.2x + -1y) * (0.2x + y)
(0.2x * (0.2x + y) + -1y * (0.2x + y)) = 0
((0.2x * 0.2x + y * 0.2x) + -1y * (0.2x + y)) = 0
Reorder the terms:
((0.2xy + 0.04x2) + -1y * (0.2x + y)) = 0
((0.2xy + 0.04x2) + -1y * (0.2x + y)) = 0
(0.2xy + 0.04x2 + (0.2x * -1y + y * -1y)) = 0
(0.2xy + 0.04x2 + (-0.2xy + -1y2)) = 0
Reorder the terms:
(0.2xy + -0.2xy + 0.04x2 + -1y2) = 0
Combine like terms: 0.2xy + -0.2xy = 0.0
(0.0 + 0.04x2 + -1y2) = 0
(0.04x2 + -1y2) = 0
Solving
0.04x2 + -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.
0.04x2 + -1y2 + y2 = 0 + y2
Combine like terms: -1y2 + y2 = 0
0.04x2 + 0 = 0 + y2
0.04x2 = 0 + y2
Remove the zero:
0.04x2 = y2
Divide each side by '0.04'.
x2 = 25y2
Simplifying
x2 = 25y2
Take the square root of each side:
x = {-5y, 5y}
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