Completing the Square using Fractions

Take one half of - and then square that answer which = and add to both sides

+ = - +

Combine like terms on the right to get

and then subtract that from both sides to get

can be reduced to so that

Eliminate the fractions by multiplying it all by 2 and then instead of completing a square I've completed a large useless circle as I arrive back at the original equation.

Now, I also used as the square of half of but eventually it also ends up as

on the left hand side of the equation.

I did this problem with the quadratic formula in about 45 seconds but I have to learn it this way. If nothing else my LaTex skills have been markedly improved in this post.

Any help is appreciated. Thanks.

Re: Completing the Square using Fractions

Re: Completing the Square using Fractions

Your error occurs right about here:

Until this point, you had done everything right. Without doing anything else, the left-hand (only) can be factored into a product of squares. The right is a number, which we can find the square root of. First I'm going to rewrite this after simplifying the right-hand side.

+ =

Now we can factor the left-hand side (AS IT IS RIGHT NOW).

Now that it is in this form, we can take the square root of both sides. We are left with

remember that every number has two square roots...

If we subtract, . If we add, we have . Thus

I go over the conceptual logic of completing the square in this video.

Re: Completing the Square using Fractions

Thank you both so much. It's always right in front of my face. Thanks again.