ax^2+bx+c=0

When solving these problems you see in the show me how that four is to play in the top part of the problem to multiply by and two on the bottom. This is given in many of the problems so it must be a set way of solving, but could you explain why this is?? I get to the point that I just want to understand my way and lately that has come a lot harder than before. I do not see that major concept here, but see I need it to solve properly.

Question

ax^2+bx+c=0

When solving these problems you see in the show me how that four is to play in the top part of the problem to multiply by and two on the bottom. This is given in many of the problems so it must be a set way of solving, but could you explain why this is?? I get to the point that I just want to understand my way and lately that has come a lot harder than before. I do not see that major concept here, but see I need it to solve properly.

anonymous · Answer

are you asking how to derive the quadratic formula?  in other words why is the solution to 
$$ax^2+bc+c=0$$
$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$?

anonymous · Answer

yes

anonymous · Answer

if you "complete the square" keeping track of all the steps, that is what you will get

anonymous · Answer

could you solve 
$$2x^2-25x+33=0$$ by completing the square rather than factoring or using the formula directly?  if you write out all the steps  you will see where the 
$$b^2-4ac$$ and where
$$2a$$ come from

anonymous · Answer

if it is not clear how to solve the formula by completing the square, then it will not be clear where the formula comes from.  they are one and the same

phi · Answer

If you like algebra, here is a derivation of the quadratic formula.  If you follow it, you see it's one of those, "that's the way it turns out" kind of things.