Solve for x. round your answer to the nearest tenth.

Perpendicular from the center to the chord, bisects it!
DE = DF/2 = 12
To find R, use Pyth Th in triangle AOB. ( AB = 10)
10^2 + 14^2 = R^2
100+ 196 = 296 = R^2
In triangle DOE 
x^2 + 12^2 = 296
x^2 = 296-144 = 152
x = √152
x = 12.3