Domino filled

The puzzle is impossible to complete. A domino placed on the chessboard will always cover one white square and one black square. Therefore a collection of dominoes placed on the board will cover an equal numbers of squares of each colour. If the two white corners are removed from the board then $30$ white squares and $32$ black squares remain to be covered by dominoes, so this is impossible. If the two black corners are removed instead, then $32$ white squares and $30$ black squares remain, so it is again impossible.

Note that each domino must cover a light square and a dark square. Because there are only $30$ light squares remaining and $32$ dark squares, it is impossible to cover all of the squares.