Hello bwhit132Welcome to Math Help Forum!

There are two answers to your question. The first answer is to do withhowit works; the second is to do withwhy. The rule explaining the how is:

- We mayadd the same number to both sides of an inequality, and it remains true. In other words:

What's happened, then, is that 4 has been added to both sides of the inequality:

That washowthe + 4 appeared.

But you may have asked:whyshould we want to add 4 to both sides of the inequality? The answer is that we need to create a term in so that we can establish the truth of .

So that'swhythe + 4 appeared.

The same thing happens again in the next stage, although it's not so clear this time. Let me put things the other way round, and you'll see how it works.

So, writing this the other way around, we get:

whenever

If we now add to both sides of , we get:

So that's thehow. Now for thewhy. Why look at at all? Well, it's to do withcompleting the square, because, again, we need to create a term in to establish the truth of .

And to make into we need to involve , because .

Is that OK now?

Grandad