The board of county commissioners, at the time and place mentioned in the notice of hearing or at the time or times to which the hearing on said petition may be adjourned, shall proceed to hear the petition and all evidence submitted against and in support of the same. The board of county commissioners shall have full authority to adjourn the hearing from time to time not exceeding four weeks in all and to grant or reject the petition, and to determine the matter; any irregularities or omissions in the allegations of the petition shall not be held or construed to deprive the board of county commissioners of jurisdiction and authority to consider and determine the matter of any such petition accepted by it for consideration and said board of county commissioners shall have full authority to make such independent investigation of the matter of such petition as it shall deem advisable and to base its judgment on such independent investigation as well as upon the evidence submitted for and against the petition upon a hearing thereon as hereinafter provided.