#### Answer

The equation has one rational solution.

#### Work Step by Step

$x^{2}+4x+4=0$
The discriminant is given by $b^{2}-4ac$. For this equation, $a=1$, $b=4$ and $c=4$
Let the discriminant be $D$. Substitute the known values into the formula and evaluate:
$D=4^{2}-4(1)(4)=16-16=0$
Since the discriminant is equal to $0$, the equation has only one solution and it is a rational number.