#### Answer

$16$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To determine the number that will complete the square to solve the given equation, $
x^2+8x+11=0
,$ use first the properties of equality to express the equation in the form $x^2+bx=c.$ Once in this form, the needed number to complete the square of the left side is equal to $\left( \dfrac{b}{2} \right)^2.$
$\bf{\text{Solution Details:}}$
Using the properties of equality, in the form $x^2+bx=c,$ the given equation is equivalent to
\begin{array}{l}\require{cancel}
x^2+8x=-11
.\end{array}
In the equation above, $b=
8
.$ Using $\left( \dfrac{b}{2} \right)^2$, the number that will complete the square on the left side of the equal sign is
\begin{array}{l}\require{cancel}
\left( \dfrac{8}{2} \right)^2
\\\\=
\left( 4 \right)^2
\\\\=
16
.\end{array}