Let me give you the method to solve x^2 + bx + c = 0. Answer: solve (x + b/2)^2 - b^2/4 = - c instead. Why, you ask? Well, first of all because some long-dead

Let me give you the method to solve x^2 + bx + c = 0. Answer: solve (x + b/2)^2 - b^2/4 = - c instead. Why, you ask? Well, first of all because some long-dead bloke figured out this neat trick and it would be a shame not to use it. And secondly it is easy arithmetic to figure out that this is an equivalent problem, so if you solve it then it certainly gives the right answer. Maybe it is just me, but if you cannot grok this then I think that your difficulties with mathematics are not curable by spending more time trying to develop intuition on this particular problem. And therefore I fail to see what Professor Loh brings to the table here. Edit: it appears that my position is being misunderstood. I do not think that someone who does not grok this argument will never be able to properly learn mathematics. I think that they should instead focus on things like logic and arithmetic and, for this particular subject, on playing with quadratics (plotting them and finding their extrema, for example). Any dressing up of the above argument for the quadratic formula is, again in my view, akin to trying to 'develop intuition' for something like the third digit of pi - it is just what it is (4 I think).