[0645] Flashbacks
└ posted on Monday, 29 December 2014, by Novil
- Sandra: Luna, you asked quite a few very weird questions in math today again.
- Luna: … Sorry.
- Sandra: Should I come over after school to help you study?
- Luna: That would be very kind. Thank you.
- Sandra: No problem. We all will get something out of it after all.
- Luna: How so?
- Sandra: The screams of terror of our old math teacher when you tried to factorize 49x² – 28 + 4 on the blackboard still haunt me every night.
- Luna: The doctor said he may eventually be able to look at numbers again without getting flashbacks.
![[0645] Flashbacks](/comics/2014-12-29-0645-flashbacks.png "[0645] Flashbacks")
is it me or is there a typo?
In panel 4 Sandra says “The screams of terror of our old math teacher when you factorized 49x² – 28x + 4 on the blackboard still haunt me every night.”
but, in the text box she says “The screams of terror of our old math teacher when you factorized 49x² – 28 + 4 on the blackboard still haunt me every night.”
so what exactly did she do wrong?
also I don’t think it’s a good idea to tell someone that they were asking weird questions in a class, if anything they should ask more if they don’t understand , but this is just a comic so…idk lol
darkrai444 wrote:
[Insert “Not sure if…” meme here] are you trolling further? (are trolls even welcome here?) could it be you didn’t understand what Crestlinger was saying? just in case it’s not apparent, Crestlinger [I believe] was saying that is how Luna tried to answer on the board… that is, incorrectly… I hope I’m not wasting my time there…
@ MathAddict: Actualy it can’t be that because it would equate to + 24X because a negative times a negative equates into a positive. The correct way would be (7x + 2)(7x – 2)
Crystalgate wrote:
I was. Even before 13 that actually. That’s somewhere in fourth to sixth grade level for us (I’d need to find an old schoolbook of mine to exactly name the year), so about age 10-12. But that might be a question of different school systems (I’m Swiss).
b>Samwise Clemens wrote:
He started of his comment with: “Probably answered along the lines of…”
So you can even omit the “I believe”. It was his intention to present a completely wrong solution all along.
Commander Clash wrote:
Actually, that would give you 49x² -4. What MathAddict wrote is absolutely right. -14x (7x times -2) plus (not times) -14x equates to -28x. And -2 times -2 to +4 as we have above.
@ shazz_smifff:
Good eye! I had to read even your comment several times until I caught that missing “x”!
Novil wrote:
The transcript still says
49x² – 28 + 4while the image says49X² – 28X + 4…When I was in highschool I use to drive my math teachers up a wall because I could do problems like this in my head and refused to ever show my work. Oddly enough no one ever accused my of cheating, I wasn’t be still I find it weird.
Aleck493 wrote:
Know that feeling. I onced use the internet to help me with math and only wrote the answer. And the teacher accused me of “cheating off my classmates”
I looked at the equation and thought “Mitternachtsformel”! (=quadratic formula. The German word translates to “midnight formula”, because you should be able to recite it instantly even when you are woken up in the middle of the night).
It is used for equations of the type
ax^2 + bx +c = 0
and the formula is
x(1/2) = ( -b +- sqrt(b^2 -4ac) ) / 2a
(there’s also an alternative called the p-q-formula)
Whenever I was confronted with an equation like this in school ( a “quadratic equation”) I was expected to use this formula to solve it. And my guess would be that in the described maths lesson, the students were expected to do the same.
I reckon Luna was asked to “solve” 49x^2-28x+4 and randomly factorized it, rather than using the formula as expected.
I want to ask the Wolfram team to add a complexification option, where you insert a simple equation and then it is made extremely complex and convoluted.
Depending on what chalk was used, it may very well have haunted my nightmares as well.
@ CDRom11:
Exactly. :>
@ darkrai444:
Hehe, got another one :>
X = 2/7 (Only one possible solution exists, since (b*b) – 4*a*c = 0 in this case.)
Do I get a cookie? 🙂
Um. How old are these kids supposed to be? I don’t understand that!
I was the kind of math student who could easily do all they put in front of me on paper, but I could barely solve for x in x^2 = 4 if asked to do it on the blackboard. Let’s just say that the college math class that had a final exam based on choosing one problem and doing it on the blackboard was not pleasant.
Remember when this comic was about Sandra and Woo? Pepperidge Farm remembers.
I think it would go (7x-2)(7x-2)=0. Then since 7x-2 is zero, you add 2 to both sides to get 7x=2. Then divide by 7 on both sides. Then x = 0.28571428571. I’m not sure if that’s right, but I think that’s how you solve it.
now that the comic had been corrected to factorize not expand 8)
the easy way recognize the perfect square pattern a² −2ab + b² = (a − b)²
49x² − 28x + 4 = (7x)² − 2(7x)(2) + 2² = (7x − 2)².
You you fail to spot the pattern you can still use the ac method to factor via grouping which given ax² + bx + c then find the factors of the product ac that sum to b and use them to fact via grouping
49x² − 28x + 4
ac = 49 * 4 = 196
-14 * -14 = 196
-14 + -14 = -28 = b
∴ 49x² − 28x + 4 = 49x² − 14x − 14x + 4
now factor via grouping
∴ 49x² − 28x + 4 = 7x(7x − 2) − 2(7x − 2)
∴ 49x² − 28x + 4 = (7x − 2)(7x − 2)
∴ 49x² − 28x + 4 = (7x − 2)²
You math people are making my brain hurt.
Jk8z wrote:
12. and And Factoring Quadratics is part of Algebra I, which is typical a high school course
Besucherin wrote:
You not expected to be taught the Quadratic Formula until after you have mastered Factoring and even after completing the square as it’s a short cut that only works in a narrow set of circumstance where you need the based skills more often.
Second it only works with EQUATION what we have here EXPRESSION, expressions have no equal sign and can not be solved.
pip25 wrote:
No cookie for you as x can be anything.
x = 2/7 is only true if 49x² − 28x = 4 = 0 note the problem does NOT say it equals anything.
roguebfl wrote:
Not always. I took Algebra in 7th grade at my junior high school (though I think the other students in the class were 8th-graders). In 8th grade, I went to a nearby high school for Geometry, then back to the junior high school for my other classes. I was able to factorize the expression in my head before reading the comments, but I still don’t get why it would cause the teacher to scream in terror.
MauveCloud wrote:
Well 7th Grade typically Pre-algbra, but that mostly linear algebra not quadratic algebra 8) But hey given she’s in Sandra’s class it could be an advanced class.
as why the scream in horror? perhaps Luna was trying to use non-euclidean geometry and started drawing elder signs 8)
Awww well ain’t that excessive?
Ruto wrote:
Sounds to me like an H.P. Lovecraft reference would be more apropos.
(My Little Luna: Mathematics is an Eldritch summons!)
It’s a good thing I took six years of math in high school. I’ll be here when there’s some calculus to solve.
I don’t understand this one. The problem itself is super easy to solve (like, I solved it in my head while reading it, basically) so did this girl pull an Emily from QC?
@ Chris W:
http://www.questionablecontent.net/view.php?comic=2853
Umm… guys, don’t you remember that Luna gets read some of the most complex maths/physics stuff around as a bedtime story?
My guess is that she didn’t get it wrong, she just got it far too right and over-thought it (maybe going into the complex plane and a few other dimensions)
Anyway, my screams of terror are filling this room as I hear that some of you want this to be an equation which can be solvable for X… it isn’t. The quadratic formula would give you the real answers for X if the equation = 0, but it will not help to factorise… just recognise the patterns is the easy way to do it.
(49 only has 1*49 or 7*7 as whole number factors… since the next term is 28, I’m going to ignore 1*49… 4 has 1*4 and 2*2, (and the negative equivalents of course). 1*4 doesn’t work when factored in (7x-4) (7x-1) = 49x^2 – 35x + 4. So the answer that should be right if it factorises nicely is (7x-2)(7x-2)… which works BTW.
Sorry, it’s a bit convoluted as most of my posts are, but oh well. I know my method is a bit wishy washy, but that’s how I go about it in my head and I can factorise most quadratics within a few seconds of looking at them.
Factorize 49x^2 – 28x + 4? That’s not that hard at all.
Wait they’re just 6th graders….
To Novil:
Congratulation for the successful nerd sniping. In this case, math nerd.
For you who don’t know what nerd sniping is: http://xkcd.com/356/
@ JuyJuka:
It says factorise so the answer is 7X(3… wait no this doesn’t work with the + 4
Never mind, quadratics so (7X-2)(7X-2)@ OneGuy:
@ JuyJuka:
I factored it in a second. 7x-2
Y? wrote:
That’s Yuna not Luna 8) Yuna is not in Sandra’s class 8)
@ Autoskip:you can’t without a “y”
(-7x+2)2
Preadatordetector wrote:
This was supposed to have the second 2 superscripted to become an exponent.
Aleck493 wrote:
I didn’t exactly drive my teacher crazy. But he was constantly chastising me for only ever writing the solution, not how I reached it. And when I told him I had solved it completely in my head said “I know. Just write down some of the steps in between as if you’d solved it on paper.”
Still prefer to do as much as possible in my head. You throw a 17 times 32 my way or something similar and I’ll have it solved faster than most people need to get out their calculators. Also never a fan of programmable calculators. Always used a solar powered one without any programmable functions and instead a formulary in paperform where necessary. Still faster and just as if not more correct than most people with their fancy programmable ones. It’s not that I was that extraordinary talented, I’m a bit above average, no more. I just had enough practice in doing this stuff in my head, that’s all there is to it.
roguebfl wrote:
Interesting. That’s quite a ways later than in our school system then. But is it really the same in all the States?
Dear God you all are making me feel old and stupid. Math was never my strongest subject but I literally look at that and have no clue what my first step would be to solve it.
Granted, I’m looking at this 2.5 decades after graduating high school but I didn’t think all my higher math skills had crumbled to dust.
Guess who just got proved wrong? This guy!
Still a fun stript though.
Lukkai wrote:
Same, though I eventually WAS forced to bend to my teacher’s will and show some of the steps.
…Also, while I used to have a mental calculator for things like 15 x 13 in my head that was faster than a real calculator, that’s a skill I needed practice on. Generally now it takes me too long, so it’s either a computer calculator, or whatever I wanted the calculation for in conversation is lost until I can bring it back up.
@ Aleck493: Yup, same here. IMHO, if you can’t do this in your head by the time you get to high school level, you’ve got no business in doing anything related to math. Factorizing/expanding quadratic expressions is 5th or 6th grade stuff.
Yet, I know lots of people who finished our equivalent of high school without being able to add fractions or solve simple equations correctly. And they even had quite acceptable marks…
Sorry, I think I’m lost. Are they saying she absolutely butchered the equation? If so, I want to know just HOW she did it in a manner that managed to make such trauma happen.
@ I’ll Eat Yourself:
I agree. Is the joke that the teacher was really bad at Math?
Lukkai wrote:
I can not Handling say for all states given it handled at the local level but roughly true but i’m sure you could find exception at least on the individual school level. However one of the Goals of Common Core is to have it students finish Algebra I by 8th Grade
@ Crystalgate:
Don’t know about the US, but in Germany you *are* supposed to get this at age 13 – at least we had binomials and quadratic equations in middle school math, 7th form. I distinctly remember as we moved house that year – the new school was a few weeks ahead in the curriculum, so I had to learn this in a hurry.
Holy cow people. There never was an equation with an equal sign.
The original goal was to find the factors of 49x^2 – 28 + 4:
7 * 7 * x * x – 2 * 2 * 7 + 2 * 2
Or if you simplify it first then 49x^2 -24 has these factors:
7 * 7 * x * x – 2 * 2 * 2 * 3
Some people seem to think the original should have been 49x^2 – 28x + 4
In which case the factors would have been:
( 7x – 2 ) ( 7x – 2)
However they all wanted to solve for x which is impossible unless the expression equals
some number. The extra x, the equal sign, and the number were not given.