Answer
x=$-2y$
Work Step by Step
$x^{2}+4xy+4y^{2}$
=$x^{2}+2xy+2xy+4y^{2}$
=$x(x+2y)+2y(x+2y)$
$(x+2y)(x+2y)$$=0$
$(x+2y)^{2}$$=0$
x=$-2y$
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