Algebra: 10^23 + [blank] * 10^23 = 10^25

I have this problem:

10 to the 23rd + ________ * 10 to the 23rd = 10 to the 25th

I know that multiplication must be done before the addition because there are no ().
I know that when you multiply numbers with exponents then you add the exponents. So if I put 10 squared on the line then I would end up with
10 to the 23rd + 10 to the 25th on the left of the = sign. but that can't be right.
I'm just getting more confused.

\(\displaystyle \L\begin{array}{rcl}
10^{23} + 10^{23} X & = & 10^{25} \\
10^{23} \left( {1 + X} \right) & = & 10^{25} \\
\left( {1 + X} \right) & = & 10^2 \\
X = 10^2 - 1 \\
\end{array}\)