the x^2 + 10x = 39 thing: the solution to which you found the geometry more appealing is called "completing the square". Algebraically, what you do is to realize that (x+5)^2 is x^2 + 10x + something else, and then you write the left side with the something else and simplify, getting (x+5)^2 = something, and then take square roots. Specifically, x^2 + 10x = 39 => (x+5)^2 - 25 = 39 => (x+5)^2 = 64 => x + 5 = 8 => x = 3 (or -13, but the original problem couldn't have a negative answer).
The geometry makes it rather more obvious why the name is what it is.
ooh, now that's a term I haven't heard since early high school... at some point I might've even remembered the operation... nowadays I'm surprised I still remember the quadratic equation and I guess I must've deliberately forgotten the special case solutions once I learned the general one
“It’s really really hard to write clearly, and if I have to write a page of context and filters to describe the data I want, I might as well be writing SQL.” True, that. I spent years going in the both directions working as a mortgage backed securities lawyer. (Guilty.) The drill was that bond traders came up with some new twist on cash flow slicing and dicing and sold it to buyers. The modeler in the back office expressed it in spreadsheet form to confirm that it worked mechanically and there would be a call to discuss it all in general terms. From there one of us lawyers would describe it in detail for the offering document and the other for the contractual document, in even greater detail. After closing, the cash flow administrator would program the whole process to determine who got what each month. At the insistence of our tax lawyer, who had a PhD in math, our work was all done with defined terms, making our work a Lego-like word problem. So, sort of like writing 10-20 pages of context and filters as the defined terms. It was fun, sort of like flipping burgers--hundreds of billions served. Until the music died.
gyah that's like the ultimate horror .... laying out a complex calculations/operations in binding contract legalese form. hats off to you for having to work with those and surviving
the x^2 + 10x = 39 thing: the solution to which you found the geometry more appealing is called "completing the square". Algebraically, what you do is to realize that (x+5)^2 is x^2 + 10x + something else, and then you write the left side with the something else and simplify, getting (x+5)^2 = something, and then take square roots. Specifically, x^2 + 10x = 39 => (x+5)^2 - 25 = 39 => (x+5)^2 = 64 => x + 5 = 8 => x = 3 (or -13, but the original problem couldn't have a negative answer).
The geometry makes it rather more obvious why the name is what it is.
ooh, now that's a term I haven't heard since early high school... at some point I might've even remembered the operation... nowadays I'm surprised I still remember the quadratic equation and I guess I must've deliberately forgotten the special case solutions once I learned the general one
“It’s really really hard to write clearly, and if I have to write a page of context and filters to describe the data I want, I might as well be writing SQL.” True, that. I spent years going in the both directions working as a mortgage backed securities lawyer. (Guilty.) The drill was that bond traders came up with some new twist on cash flow slicing and dicing and sold it to buyers. The modeler in the back office expressed it in spreadsheet form to confirm that it worked mechanically and there would be a call to discuss it all in general terms. From there one of us lawyers would describe it in detail for the offering document and the other for the contractual document, in even greater detail. After closing, the cash flow administrator would program the whole process to determine who got what each month. At the insistence of our tax lawyer, who had a PhD in math, our work was all done with defined terms, making our work a Lego-like word problem. So, sort of like writing 10-20 pages of context and filters as the defined terms. It was fun, sort of like flipping burgers--hundreds of billions served. Until the music died.
gyah that's like the ultimate horror .... laying out a complex calculations/operations in binding contract legalese form. hats off to you for having to work with those and surviving