This (arguably unhelpful) phrase seems to be taught across schools all over the world. What are some other phrases like this that are common ?
This (arguably unhelpful) phrase seems to be taught across schools all over the world. What are some other phrases like this that are common ?
Hurr durr what if I just multiply the whole thing by 4a for some reason? Oh and then after that I’ll add b² to both sides, just for shits and giggles. And for good measure, I’ll move a few numbers from one side to the other, and that leaves me with 4a²x² + 4abx + b² = b² - 4ac.
And then golly gee! Wouldn’t you know it? That just happens to let the left side factor neatly into (2ax + b)²! So I’ll just take the square root of both sides…
No!
No!
Bad!
This is fucking voodoo. I hate this shit. It’s like trigonometric substitution.
Math is procedural. Math is algorithmic. Math is repeatable.
“If these numbers looked a little different than they do, I could solve this. Oh, wow! If I just sprinkle these magic values into my problem, everything works out great!”
Oh yes, I can see how if you just plug in this shit you pulled out of your ass, everything works out great! But when you aren’t around for a fecal transfer, I have no idea how to come up with that.
I was top of my class in math. But that voodoo shit never made any sense to me.
And there is absolute value of zero chance I could figure all that out in the heat of the moment if I forgot the quadratic formula. I had to work backwards from the formula to even get all that in the first place.
The derivation of the quadratic formula is nice because it doesn’t rely on anything fancy and it’s all tricks the teacher is likely to teach around the same time you’re learning it. It’s not voodoo shit, it’s just the ax^2 + bx + c = 0 and you solve for x.
Thanks for the alternative explanation. Completing the square never made much sense to me either, so I never would have arrived there.