let angles ABC = ACB = a

therefore angles ABD = BCE = - a

and since DB = BC and AB = CE

you have congruent triangles ADB and EBC (SAS)

Hence, angles ADB = EBC

also, angles EBC = XBD (vertically opposite angles)

which means angles ADB = XBD = EBC

Hence, triangle XDB is isosceles, and DX = XB.