you must use all 4 wires
you can not run just one battery wire .. the plus with out the negative
it will not be a complete circuit
many controllers are constructed using either common negative or common positive
what that means is the other side the "NON-common" connection is the one that is used to control the charging
a controller with common negative controls the PLUS side output
a controller with common positive controls the negative side output
in most solar installs using all (4) connections two for the panels , two for the batteries, the results are the same the batteries are charged as needed and the solar is isolated from the batteries by the "controlled connection"
common neg does NOT mean only (3) terminal connections
i have NOT seen that on any controller