How can you simplify the quadratic formula using completing the square?

[Robert1986]

Wait... so all of this is to avoid minus signs?

Yeah, and here's the funny thing: they don't actually go away in practice.

Are people really that scared of a -4ac?

People in general? No.

Agenredlum? Apparently very much so.

 

[Robert1986]

Finally, but it took much more than half an hour LOL. That's because we're not in the same room talking.

I looked at what you wrote and I don't see a problem with it initially, except you put a b^2 where it didn't belong, but that doesn't matter to me because it did not affect your final result.

x = [b' +- sqrt(b'^2 + 4ac')]/[2a] = [(-b)^2 +- sqrt((-b)^2 + 4a(-c))]/[2a]

My mistake.

The rest of it seems fine to me but I must caution you, I am not as rigorous as others.

Yes, I have observed.

To me, it seems a tiny bit like circular reasoning but I am no expert in logic. Let othe

It only seems that way because the result is trivial.

Don't forget that the textbook version has an extra minus sign and subtraction instead of addition. Those 2 differences are going to cause more problems. Does that make sense?

No, that doesn't make sense. I would say that writting down a completely new equation, and then using that to solve the original one will cause problems. I'm a math guy, a minus sign doesn't scare me this much.

 

[Hurkyl]

Okay, you've spent long enough trying to repeal the use of negative numbers to recognize that all of the various forms of a quadratic equation differ only superficially. Time to wrap things up.