How to convert SAT formula to 3SAT format?

Question

I have a hard time understanding what is a NP Completion. Since one of my professor didn't explain well to me on this example problem they give us. If anybody know this solution, please explain it to me so I can able to learn. Here the equation that I was having trouble on. Please take a look.

Answer 1

If you have a clause C that has too few literals, it can be replaced by (C ∨ x) ∧ (C ∨ x′) where x is a fresh variable.

If you have a clause C that has too many literals, you can first split it as C = C0 ∨ C1, putting one half of the literals in C0 and the other half of the literals in C1, then return to conjunctive normal form by replacing C with (C0 ∨ x) ∧ (C1 ∨ x′).