Brian and Jennifer each take out a loan of $x.$

Jennifer will repay her loan by making one payment of $800$ at the end of year $10.$ Brian will repay his loan by making one payment of $1120$ at the end of year $10.$

The nominal semiannual rate being charged to Jennifer is exactly one$-$half the nominal semiannual rate being charged to Brian.

Calculate $x.$

A$.562$

B$.565$

C$.568$

D$.571$

E$.574$