Answer
$y=-\displaystyle \frac{11}{2}$
Work Step by Step
$ 4y^{2}+44y+121=0\qquad$...recognize a perfect square trinomial.
$(A\pm B)^{2}=A^{2}\pm 2AB+B^{2}$
$(2y+11)^{2}=0$
$(2y+11)(2y+11)=0\qquad$...apply the principle of zero products.
$2y=-11$
$y=-\displaystyle \frac{11}{2}$
Type the equation into a graphing utility and see
that the graph intercepts the x-axis at $-\displaystyle \frac{11}{2}$.