What number would you have to add to both sides to complete the square? x^2-16x=-8

The question is about the number we need to add both sides. It is 64

This step is needed to make the left side of the equation a perfect square.  This is done by halving the linear coefficient, squaring that value, and then adding it to both sides of the equation.  In this case you would add:

(-16/2)^2=(-8)^2=64

So you would add 64 to both sides...

x^2-16x=-8

x^2-16x+64=56  now the left sides is a perfect square...

(x-8)^2=56