Trying to simplify a Boolean expression
Actually your second solution as well as the textbook solution, both are right.

I put the expression for \$X\$ into K-map:


It gives me the reduced expression as:
$$X=\overline B\overline C+A\overline B  +BC$$
$$ie.,X=BC+\overline  B(A+\overline C) $$

But I can round the 1's in this manner as well:



It gives me the reduced expression as:
$$X=\overline B\overline C+AC  +BC$$
$$ie.,X=\overline B\overline C+C(A+B) $$

First solution is what your textbook derived.
Second solution is what you derived.
Both reduced expressions are right.