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.