`4x^2+4xy+y^2+x^2+14x=0`
`<=>(4x^2+4xy+y^2)+(x^2+14x+49)-49=0`
`<=>(2x+y)^2+(x+7)^2=49`
`<=>(2x+y)^2+(x+7)^2=0^2+7^2`
`-TH_1:`
$\begin{cases}2x+y=0\\x+7=7\\\end{cases}⇔\begin{cases}x=0\\y=0\\\end{cases}$
`-TH_2:`
$\begin{cases}2x+y=7\\x+7=0\\\end{cases}⇔\begin{cases}x=-7\\y=21\\\end{cases}$