Algebra

First, let's combine some like terms!

$x^2 - 22c + c$. 

In order for this to be the square of a binomial, we need c to be the square of half the value of -22. 

Solving this, we get c = 121. 

Indeed, if we have $x^2-22x+121=(x-11)^2$. 

So we have c = 121. 

Thanks! :)