Find the roots of the following quadratic equation,if they exist,by the method of completing the square: $4x^{2} + 4\sqrt{3}x + 3 = 0$.

(N/A) Given equation: $4x^{2} + 4\sqrt{3}x + 3 = 0$.
We can rewrite the equation as:
$(2x)^{2} + 2(2x)(\sqrt{3}) + (\sqrt{3})^{2} = 0$.
This is in the form of the algebraic identity $(a + b)^{2} = a^{2} + 2ab + b^{2}$,where $a = 2x$ and $b = \sqrt{3}$.
Therefore,$(2x + \sqrt{3})^{2} = 0$.
Taking the square root on both sides,we get:
$2x + \sqrt{3} = 0$.
Solving for $x$:
$2x = -\sqrt{3} \Rightarrow x = -\frac{\sqrt{3}}{2}$.
Since the quadratic equation has a repeated root,the roots are $x = -\frac{\sqrt{3}}{2}, -\frac{\sqrt{3}}{2}$.