To find the value of c in a perfect square trinomial, apply the formula:
[tex]\begin{gathered} c=(\frac{b}{2})^2 \\ \text{ Where} \\ ax^2+bx+c\Rightarrow\text{ Square trinomial} \end{gathered}[/tex]
So, in this case, you have
[tex]\begin{gathered} z^2+22z+c \\ a=1 \\ b=22 \\ c=\text{ ?} \end{gathered}[/tex][tex]\begin{gathered} c=(\frac{b}{2})^2 \\ c=(\frac{22}{2})^2 \\ c=(11)^2 \\ c=121 \end{gathered}[/tex]
Therefore, the value of c that makes the given expression a perfect square trinomial is
[tex]c=121[/tex]
