ZFW CONTROLLER EXPERIENCED OPERATIONAL ERROR AT FL350 WHEN FAILING TO PROVIDE TIMELY SEPARATION VECTORS TO TWO CONVERGING AIRCRAFT.

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I RECEIVED A BRIEFING ON THE TURKI-HI RADAR (93) SECTOR. DURING THE BRIEFING; I NOTICED THAT ACFT NEEDED TO BE SEQUENCED WITH OTHER TFC DESTINED DFW. ACFT X WAS ON THE TXO TRANSITION OF THE UKW9 ARR TO DFW; ACFT Y WAS S OF TXO DIRECT FUZ. MY FIRST CLRNC WAS TO TURN ACFT X TO A 160 DEG HDG. I THEN WENT ON TO OTHER THINGS I HAD NOTED DURING THE BRIEFING. WHEN I EVALUATED THE STATUS OF MY VECTOR; I NOTICED THAT ACFT X WAS CONVERGING WITH ACFT Y. I TURNED ACFT X BACK ON COURSE DIRECT TURKI INTXN. AT THIS POINT; CONFLICT ALERT ACTIVATED. I THEN TURNED ACFT Y TO A 180 DEG HDG 'IMMEDIATELY.' I THEN TURNED ACFT X TO A 070 DEG HDG 'IMMEDIATELY.' THE ACFT TURNED AWAY FROM ONE ANOTHER BUT NOT SOON ENOUGH TO MAINTAIN STANDARD SEPARATION. I HAD RECENTLY BEGAN TO WONDER IF ALL THE TIME PROVIDING OJT WAS AFFECTING MY SKILLS AS A CTLR. I WOULD LIKE TO THINK I CAN DO IT ALL; BUT THIS WOULD NOT BE A SITUATION I WOULD NORMALLY MISS. I DO NOT LIKE TO TAKE CHANCES OR GIVE RISKY CLRNCS. I NORMALLY USE POSITIVE SEPARATION TECHNIQUES.