Let's take a look at a perfect square trinomial.
[tex](x+7)^2[/tex]
We can distribute this expression to get [tex]x^2+14x+49[/tex].
An important relation to recognize here is that the constant is the square of half of the x value.
Now, if we wanted to add a number to [tex]x^2+16x[/tex] to make a perfect square trinomial, we could have the value of x and then square it.
Half of 16 is 8, and 8 squared is [tex]\boxed{64}[/tex]
