Firstly, let's simplify the expression inside the brackets:
6.3 + 2.1 = 8.4.
10 - 4 = 6.
Replace these values back into the original equation, we get:
5.5+7[(8.4) X 4+(6)].
Next, we will perform the calculation inside of the brackets using our order of operations (BODMAS/BIDMAS):
8.4 X 4 = 33.6.
Then, add 6 to this number:
33.6 + 6 = 39.6.
Replace this value back into the original equation:
5.5+7[39.6].
Now multiply 7 by 39.6:
7 * 39.6 = 277.2.
Finally, add 5.5 to this number:
277.2 + 5.5 = 282.7.
Therefore, the result is 282.7.