Franz joseph, emperor of austria, agreed to the creation of the dual monarchy to

improve the economy of the empire

satisfy the demands of hungarian nationalists

increase the role of germans in the empire

gain support of the slavic minorities

The answer is to satisfy the demands of the Hungarian nationalists.  During this time there was nationalism was now growing in Hungary as they were not satisfied with Austrian rule.  Austria at the time was declining in power after the wars with Italy.  This was later dissolved after World War I.

they made rome the dominant power in the mediterranean.