Quote by Robert1986
Can I just get two questions answered, so that I understand a little more:
a) Do you think that the following equations have the same solution set:
ax^2 + bx + c = 0
and
ax^2 = bx + c
b)please post an example which uses this trick to make my life easier. I still do not see how finding the roots of ax^2 + bx + c is made easier by writting ax^2 = bx +c and then using your quadratic formula which does not give solutions to ax^2 = bx + c but, in fact, gives solutions to ax^2 + bx + c = 0. How do the added steps make it easier than just using the original quadratic formula from the getgo?

If a, b, c are particular values, example a = 1 b = 2 c = 3 then the equations above DO NOT have the same solution set. I never claimed the 2 forms above have the same solution set for PARTICULAR values.
If you consider a, b, c, abstractly, as running through all real numbers then the 2 forms above have the same solution set. TAKEN AS A WHOLE SET. I emphasize this last part because it is very important for the definition and derivation that I did.
To post 1 example would not be enough. I have to post 7, to show the way signs effect both formulas, a total of 14 calculations. I have been dreading this but i will do it. Give me some time.
My argument was the textbook definition and formula has more symbols than my version so that makes my version simpler.