Upon the filing of approval by the review board of a twenty percent annexation petition under the election method to call an annexation election, the board of county commissioners at its next meeting shall fix a date for hearing thereon to be held not less than two weeks nor more than four weeks thereafter, of which hearing the petitioners must give notice by publication once each week at least two weeks prior thereto in some newspaper of general circulation in the area proposed to be annexed. Upon the day fixed, the board shall hear the petition, and if it complies with the requirements of law and has been approved by the review board, shall grant it. The hearing may be continued from time to time for an aggregate period not exceeding two weeks.