"Factorising Quadratics" by benchen71

[benchen71]

ha ha ha ha ha yeahhh… no.
I’ll cheer the rest of you from the sidelines. ( :

As will I.

I'm with you Wendy!

For what it's worth, the nudges should help you get to the answer without having to do any actual maths! (Spoiler 5 has a link to a website that will do it for you!)

[HeadinHome]

thanks for your kind encouragement, Ben. That made me think okaaaay, I’ll try it. so, grid completed. As for the meta, completely at sea as to what some of the nudges mean, such as number 3. And regarding nudge 1, nope, just four that seem like a pattern, not five . And the link you provided .. when I tried the first one it said “does not factor” - so i’m clearly doing something wrong already (probably stems from not understanding nudge 3). Again, too much anxiety rising. HATED algebra…

Oddly, I passed calculus somehow, so at some point I was able to overcome my mathphobia enough to get the job done. But it was painful. Also, my mom was a math teacher and probably wept over me when I wasn’t looking. Poetry, now. Give me a poem to analyze and write an A+ essay on, and I’m your girl. Or I can just write a new poem on the old one. Or give me a pencil and I will happily sketch you a new home.

Thank you, STEM people. We arts people know you help make our lives better, what with your chemistry and aerodynamics and medical breakthroughs and whatnot. We shall continue to enhance the beauty of yours.

[boharr]

I never took calculus, so out of curiosity I have simplistic questions.
Why would a person factor and not solve?
Is there a difference?
If so, what is it?
Can these questions be answered in words only?

[woozy]

ha ha ha ha ha yeahhh… no.
I’ll cheer the rest of you from the sidelines. ( :

As will I.

I'm with you Wendy!

For what it's worth, the nudges should help you get to the answer without having to do any actual maths! (Spoiler 5 has a link to a website that will do it for you!)

Oh.... I didn't realize the three entries in a row were supposed to actually physically make an equation... I just viewed them as steps of manipulations

with that in mind here's a nudge specifically for Headin' Home for the FXF, ONEF, SIX trio of entries enter "f^2 + 1f = 6" into the factor machine and if it does what is says you should do fine and get (f-2)(f+3)=0.

EDIT: The machine didn't do as I predicted. If you enter "f^2 +1f = 6" into the machine it solves (not factor) and spits out (correctly) "f=2 or f=-3". What you should enter is "f^2 +1f -6" (which is an phrase, not a sentence) then (since it is a phrase and not a sentence) it will factor (parse) the phrase rather than solve (simplify) the sentence, and spit out "(f-2)(f+3)".

I think there is a not more going on than a "use an app" advice can accomodate

END EDIT

Or... you can do

f^2 + 1f = 6

f^2 + 1f - 6 = 0

Think of the factors of 6: (1x6, 2x3) and check which of them are have a difference of 1. 1-6 = -5. No. 2-3 = -1. No.. 3-2=1. Yes. 6-1 = 5. No. To get

f^2 + 1f -6 = 0

(f-2)(f+3) = 0

[woozy]

All said and done I think nudges 3-5 forget just how much thought and practice and comfort is required to even comprehend the task.

[StunGun]

So I got through all the steps to the last nudge on my own. But flummoxed. Any gentle hints on where to go after nudge 5?

[StunGun]

Got it.
Inspired puzzle!

[KayW]

Nudged across the moat.

Needed nudges - I went too far with gazintas (factoring) and not far enough with ciphering (letter decrypting)

Thanks, Ben! That's more algebra than I've done in decades

[benchen71]

Another solver update, since I have a spare moment:

JR
SeamusOL
sw3aterCS
Schmeel
mxa
Mr Tex
Tim
Account
Sharkicicles
MrTheHan
KayW

We're up to 37 now!

[MikeyG]

I never took calculus, so out of curiosity I have simplistic questions.
Why would a person factor and not solve?
Is there a difference?
If so, what is it?
Can these questions be answered in words only?

I thought this was a limerick at first, haha.

[boharr]

I never took calculus, so out of curiosity I have simplistic questions.
Why would a person factor and not solve?
Is there a difference?
If so, what is it?
Can these questions be answered in words only?

I thought this was a limerick at first, haha.

You don't recognize a quadraticialzed rhyme scheme? The I's are imaginary words. haha

[Joe Ross]

@boharr

Once the grid is filled, it becomes obvious to the casual observer...

[hoover]

I never took calculus, so out of curiosity I have simplistic questions.
Why would a person factor and not solve?
Is there a difference?
If so, what is it?
Can these questions be answered in words only?

I thought this was a limerick at first, haha.

There once was a mathematician...

[MMe]

"Solving" is finding the roots of the quadratic equation, which means determining the values of its variable for which the polynomial function equals zero.

"Factoring" is expressing the polynomial function (e.g. x^2+5x+6) in a different form , as a multiplication of factors (e.g., (x+3)(x+2)). That can be useful in solving an equation in more than one way. For example, if you know that (x^+5x+6)/(x+3) = 3, then factoring quickly gives you x+2=3, and so x=1 -- without needing to haul out the quadratic equation.

[benchen71]

Another solver update for you:

ChrisCross
Philip Chow
Rick
zmaj
LasersharpAurora
James

That's 43.

[woozy]

There once was a mathematician...

whose wits were subject to attrition
while modelling migration
he used Lebesgue integration
when he should have just stuck to addition

[benchen71]

Some more solvers, bringing us up to 50!:

Jerry Miccolis
JM
Cate C3
kamashdad
rayyandroid
Sanne
Darth

Final update before the answer reveal, Monday morning Australia time!

[ReB]

Crossed the MOAT. Well done.

[benchen71]

Two more solvers, bringing us up to 52, which is pretty good for a "week 4":

ReB
SJ

[benchen71]

And now for the solution reveal!

Here's the solution to "Factorising Quadratics":

I was fascinated by how many 10-letter mathematicians there are: for example, Pythagorus, Fibbonacci, Archimedes, Von Neumann and Alan Turing were names I could see as meta submissions. However, there was a good reason for the answer being DIOPHANTUS.

From Wikipedia:
"Most of the problems in Arithmetica lead to quadratic equations. Diophantus looked at 3 different types of quadratic equations: ax2 + bx = c, ax2 = bx + c, and ax2 + c = bx. The reason why there were three cases to Diophantus, while today we have only one case, is that he did not have any notion for zero and he avoided negative coefficients by considering the given numbers a, b, c to all be positive in each of the three cases above."

The 5 equations encoded into the puzzle all fit Diophantus' first case. However, by using algebraic notation (rather than a purely geometric method) and factorising as shown, we can go beyond Diophantus by recognising that these equations also have negative solutions.

Interestingly, if you've heard of "Fermat's Last Theorem", Pierre de Fermat wrote this in the margin of a copy of Diophantus' book. Special shoutout, therefore, to @merlinnimue who commented on Crosshare: "I have discovered a truly remarkable solution to this meta puzzle, but unfortunately this text field is too small to contain it." Love it!