To make the expression $49x^2+\frac{1}{49x^2}$ a complete square, we need to add a term that fits the form $(a+b)^2 = a^2 + b^2 + 2ab$ or $(a-b)^2 = a^2 + b^2 - 2ab$. Here, $a^2 = 49x^2$, so $a = 7x$. And $b^2 = \frac{1}{49x^2}$, so $b = \frac{1}{7x}$. The term to be added is either $2ab$ or $-2ab$. $2ab = 2 \times (7x) \times (\frac{1}{7x}) = 2$. And $-2ab = -2 \times (7x) \times (\frac{1}{7x}) = -2$. Thus, the terms that can be added are 2 and -2.