Question

What value should be added to the expression to create a perfect square?

Answer 1

Let's take a look at a perfect square trinomial.

$(x+7)^2$

We can distribute this expression to get $x^2+14x+49$.

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 $x^2+16x$ 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 $\boxed{64}$