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Question

Complete the square to solve the equation for x: ax^2+bx+c=0. Provide a detailed account of your procedures.

Don't get the procedures. part

Answer 1

This question has been submitted twice and has already been answered.

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Ah, that is because you do not like the answer provided!

Either Mark or I will be happy to answer any specific question about the problem you have submitted...but neither of us will do all your work for you!

Did you ever do a so-called 2 column proof (e.g. in plane geometry)?

That is essentially what is required here.

And when you do it you will have derived the quadratic formula.

I will start you out:

ax²+bx+c=0

Divide the equation by a (assuming that a≠0).

x²+(b/a)x+(c/a)=0

Subtract c/a from each side.

x²+(b/a)x=-c/a

Complete the square by adding b²/4a² to both sides.

And if you don't know why this is done, you should read about the process of completing the square.

x²+(b/a)x+(b²/4a²)=[x-(b/2a)]²=(b²/4a²)-(c/a)

You should now be able to go on and complete the derivation with some straight forward algebra.