Can someone solve this sudoku without trial and error?

A simple hint:

This technique is called a naked pair; it seems you've used it already in row 7 to eliminate the 9's in row 4 and 6.

We can solve this puzzle with two sudoko techniques.

First with Naked Pair (already @Glorfindel discussed). This one will fit with column $6^{th}$, where $2$ and $9$ will follow the naked pair, and remaining $2$ and $9$ from column $6^{th}$ would be eliminated.

second with XY-Wing, where R6C5, R7C3 and R7C6 fit for the XY-wing technique. We will choose $7$ from R6C5, and this number will fit (other number $2$ from R6C5 will not fit here). Please see the below in the picture.

Final solution looks like.

It can be solved with elementary techniques. Using my solver (CSP-Rules, available here: https://github.com/denis-berthier/CSP-Rules-V2.1):

naked-pairs-in-a-column: c6{r2 r8}{n2 n9} ==> r7c6 ≠ 2, r3c6 ≠ 2, r1c6 ≠ 9

biv-chain[2]: r2n9{c7 c6} - c5n9{r1 r4} ==> r4c7 ≠ 9

whip[1]: b6n9{r5c9 .} ==> r5c4 ≠ 9`

biv-chain-rc[4]: r3c4{n5 n2} - r7c4{n2 n7} - r7c6{n7 n4} - r9c6{n4 n5} ==> r3c6 ≠ 5, r9c4 ≠ 5

singles to the end