Let's work backwards.
The answer will be in the form (x+a)^2 for any real number a
Now the expansion will be x^2+2ax+a^2.
We can see just from this that 2a=5/4
a=5/8
The result binomial should be x+5/8
Resulting binomial squared expansion should be x^2+5/4x+25/64
The term we need to add will be 25/64
