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Submitted on
March 29, 2014
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Lyra's calification by Pandramodo Lyra's calification by Pandramodo
:iconlyraponyplz::iconsaysplz:problem? :iconhiddentrollfaceplz:
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inda26 Featured By Owner Jan 2, 2015  Hobbyist General Artist
im just sayin 42......
Scarecrow8642 Featured By Owner Nov 13, 2014  Hobbyist Digital Artist
*cough* Eleven *cough*
sonicthebone Featured By Owner Nov 5, 2014  Hobbyist Digital Artist
I love your art style! And also I'm utterly confused by this.
cutegirl4875 Featured By Owner Oct 31, 2014  Hobbyist Artist
What?!! Pinkie Pie Scream01 
Videogeek95 Featured By Owner Oct 3, 2014
...I only took Pre-Algebra my Senior Year... So I'm utterly fucked...
rainbine1234 Featured By Owner Sep 29, 2014  Professional Traditional Artist
:iconlyraponyplz::iconsaysplz: NAILED IT
crazycandyfan Featured By Owner Sep 28, 2014  Student Artist
Damm it Lyra I don't know math!!!!!!!!! 
TheScribbleArtCreeps Featured By Owner Sep 13, 2014  Student Artist
im not a expert in math!!!!!
Daniel1944 Featured By Owner Sep 12, 2014
Y asi es como se creo las mates en ponyville
TK (Yo wassup) [V1] TK (Yo wassup) [V1] TK (Yo wassup) [V1] 
Master-slayer1991 Featured By Owner Aug 30, 2014
when i did this i got a 11 can it go that high?
bluefoxycat Featured By Owner Aug 16, 2014  Hobbyist Digital Artist
Whooves' face. That's all, folks.
DragonFUA11 Featured By Owner Aug 7, 2014
.... -R!
StargazerDesign Featured By Owner Jul 25, 2014  Hobbyist Interface Designer
Math is complicated... 
LeapingPony Featured By Owner Jul 29, 2014  Hobbyist Digital Artist
Ohh, if think is SO Complicated.. Then Answer These Questions.... (U Can Say IDK I Don't Know If Want To)

79 + 51 - reciproc(86) = ????

sqrt (915) = ??????

See? easy.... :3
StargazerDesign Featured By Owner Jul 29, 2014  Hobbyist Interface Designer
Thank you for the explanation, but I REALLY hate math. ;D
LeapingPony Featured By Owner Jul 31, 2014  Hobbyist Digital Artist
Okay... :P
Cooper31 Featured By Owner Jul 25, 2014  Student Digital Artist
Exploding maths problem!
Speedy526745 Featured By Owner Jul 24, 2014  Hobbyist Digital Artist
Is it bad that I immediately tried to solve this equation as soon as I saw it?

And here's the breakdown, because that's how I roll:
x + sqrt(x - 1) = 2x – 7

sqrt(x - 1) = x – 7

x – 1 = (x - 7)2 = x2 – 14x + 49

0 = x2 – 15x + 50

0 = (x – 5)(x – 10)

7 ≠ 3, so x ≠ 5

13 = 13, so x = 10  


Swampy315 Featured By Owner Oct 6, 2014  Hobbyist General Artist
uh uh uh uh uh uh uh im ashamed im supposed to be a master at math
im crying irl
angelic-rhapsody Featured By Owner Sep 12, 2014
Ok, math is one of those things I need to know, but don't.  I can follow your path up 'til the second portion of step three (is that FOIL?  I almost remember that...), and so I'm going to ask for a descriptive breakdown.

Speedy526745 Featured By Owner Sep 12, 2014  Hobbyist Digital Artist
Sure, you got it!

Yes, I in fact did use the FOIL method.  Recall that (x - 7)2 = (x - 7)(x - 7).
Normally, we would multiply the First terms in the two binomials to obtain the first term. (x - 7)(x - 7) [x * x = x2]
Next, we multiply the Outer numbers together. (x - 7)(x - 7) [x * -7 = -7x]
Then, we multiply the Inner two numbers together and add that to the outer number product to form the second term. (x - 7)(x - 7) [x * -7 = -7x; -7x + (-7x) = -14x]
Finally, we take the product of the Last terms in the binomials to get the third term. (x - 7)(x - 7) [-7 * -7 = 49]

Then combine the terms to form the result: x2 – 14x + 49

There is actually a shortcut that can be used if and only if the binomials being multiplied are the same, like in our problem.  It goes as follows:
First term: square the first term in the binomial.  [(x - 7)2 = x2]
Second term (here's the trick!): multiply the terms, then double the result.  You can remember to double this by thinking of the squared symbol as a two. [(x - 7)2 -> x * -7 * 2 = -14x]
Third term: square the last term in the binomial.  [(x - 7)2 = 49]
Combine the terms and you will get: x2 – 14x + 49

By this stage in the problem, we have:
x - 1 = x2 – 14x + 49
I subtracted 'x' and added '1' to both sides to cancel out the 'x - 1' binomial.  Now we have:
x2 + (–14x - x)) + (49 + 1) = x - 1 - x + 1 = 0
x2 – 15x + 50 = 0
This is exactly what I need to solve this using the quadratic equation.  Luckily, this one doesn't need that.  We just need to find two numbers that fit the following conditions:
1) Their sum must equal the second term (-15 in this case).
2) Their product must equal the third term (+50 in this case).
-5 and -10 meet both of these conditions, so let's try factoring by grouping:
First, we split -15 into -5 and -10, such that:
x2 – 15x + 50 = x2 – 5x - 10x + 50
Then, we group the four terms into two groups and pull out any common factors:
x2 – 5x - 10x + 50 = (x2 – 5x) + (-10x + 50) = x(x - 5) - 10(x - 5)
See how pulling out the right terms makes the two binomials identical?  This is a good thing.  Now we can combine like terms to rewrite the equation this way:
x(x - 5) - 10(x - 5) = (x - 10)(x - 5)
So now we have:
(x - 10)(x - 5) = 0
We now set each binomial to equal 0, getting two equations:
x - 10 = 0 and x - 5 = 0
Solving both gets us:
x = 10 and x = 5

Now, none, one, or both of these solutions works; to check, I plugged them back into the original equation.
x = 5 breaks the equation, because I get 7 = 3, which isn't true, but x = 10 satisfies the equation because I get 13 = 13, which is always true.
Therefore, the correct answer to this problem is [x = 10].

Sorry about the wall of text.  If you have any questions regarding this explanation, feel free to ask!  I will help you out as best as I can! 
RainbowBurn Featured By Owner Edited Oct 11, 2014
Here it is: (EDITED... I messed up)
ORIGINAL:                                     x-√(x-1)=2x-7
DERIVATIVE OF BOTH SIDES: 1- ((1/2)(x-1)^(1/2))1=2
SIMPLIFY:                                  ((-1/2)(x-1)^(1/2))=1
SQUARE BOTH SIDES:                            x-1=4

(It's a bit confusing but I got different answer, maybe it's the wrong thing to do)
(or this problem is not a good one)

RainbowBurn Featured By Owner Oct 11, 2014
Darn.. I was WAY over thinking it. I would have done the Derivative of both sides, using the chain rule on the left.
angelic-rhapsody Featured By Owner Sep 13, 2014
Thanks for that wall of text!  I think I'm following it better now.  I do have a couple questions, though (Gad, I feel slow):

1.  When subtracting x and adding 1 to both sides, are we just following the symbols to where we apply the change (i.e.: minus x goes to minus 14x and plus 1 goes to plus 49), or is it something else?  If so, what?  If not, then what does one do when one or both symbols don't match, or does that even happen?
2.  I assume we split the second term into -5 and -10 because it was formed by addition to begin with, therefore the formula remains unchanged.  And the rules for selecting -5 and -10 reflect the FOIL method.  Is that right?
3.  "Binomial" is a funny word.  And this isn't a question.
4.  I admit to some confusion when you pull out the common factors in step... uh... x(x - 5) - 10(x - 5).  That is: how, exactly, does -10x + 50 translate to -10(x - 5)?
5.  I think that's all.
6.  Oh, wait!  One more (although this one is more of a 'general knowledge' bit).  In the solution description, you say, "None, one, or both of these solutions work."  In this problem, one works.  What happens when none or both work?

Seriously, though: thank you!  I know helping out some random fellow on the internet probably isn't on the Top Ten List of Things To Do Today, so I really appreciate the time you're giving me.

For serious.
Speedy526745 Featured By Owner Sep 13, 2014  Hobbyist Digital Artist
A1) In this case, the symbols matched. In general, it is combining the like terms.  If I had to add x and subtract 1 in this problem, then it would be (-14x + x) and (49 - 1), which reduce to -13x and 48, respectively.
A2) Yes, it's a legal math move to split the term into those two because it doesn't alter the problem.  I just wrote it differently for clarity.  Second, those rules do reflect the FOIL method.  The first rule refers to the term formed by the O and I steps, while the second rule refers to the term formed by the L step.
A3) :iconphineasplz::iconsaysplz: Yes.  Yes it is.
A4) -10x = (in this case) -10 * 1 * x and 50 = (again, in this case) -10 * -5.  Notice that the sign beforehand was a plus sign and the sign afterwards (inside the binomial) is a minus sign.
A5) Are you sure?
A6) If none were to work, the equation is said to have no real solution.  It does have a solution, however, but it will involve imaginary numbers, and that's a whole other topic.  If both solutions were to work, then the equation has two solutions.  On a graph, a line connecting the two values would cross the parabola formed by our original equation twice (blame the x2 term).

Hope this helps!  Again, feel free to ask questions if you still need some clarity.
angelic-rhapsody Featured By Owner Sep 14, 2014
Hmmm... imaginary numbers...…

Okay.  Yes, I think I understand this.  Thank you for helping a poor, under-educated fool understand a pony's terrible scoring habits.  A few questions popped up in the "general knowledge" category, but I think I'll not take more of your time and instead pester the Google.  And then take classes when I can.

Thanks again!
Speedy526745 Featured By Owner Sep 14, 2014  Hobbyist Digital Artist
No problem!  Happy to help!
Morrigan1235 Featured By Owner Sep 25, 2014  Hobbyist General Artist
even with the explanation I can't do it no wonder I'm failing math
PandFStudios Featured By Owner Edited Aug 24, 2014  Student Digital Artist
You're not the only one...
I tried to square both sides immediately and got stuck at

3/2x-29/2+24/x = √(x+1)...

Haven't math-ed in a while...

Btw I think you're probably right.

ThePianistDragon Featured By Owner Jul 25, 2014  Hobbyist General Artist

I did mine a little differently.
X + √(X-1) = 2X - 7  the equation on the card

√(X-1) = X - 7   getting the sqrt by itself

X – 1 ≥ 0    calculating what the x under the sqrt could be

X ≥ 1    done; the x under the sqrt has to be greater than or equal to 1

0 ≥ X – 7    knowing the end result of the sqrt has to be greater than or equal to zero we use this to calculate what x by itself should be

7 ≥ X    done; the score on the card has to be seven or more (but nothing more than 10)

X – 1 = (X - 7) * (X - 1)    multiplying both sides by  removes the sqrt

X = 7 , X ≠ 1    we already know x by itself can't be 1, so it has to be 7

X – 1 = 7    but we still have a minus one on the other side, so…

X = 8    that's better

I haven't done this sort of math in a while, so I'm not sure if I'm right. But I just wanted to show how I got it. I got 8 as my score.


Mandelbrony Featured By Owner Edited Jul 26, 2014

"0 ≥ X – 7    knowing the end result of the sqrt has to be greater than or equal to zero we use this to calculate what x by itself should be"

If sqrt(x-1) is assumed to be >=0, then the opposite (which is equal to this) must also be >=0.  so we conclude that x-7 >= 0.

"X – 1 = (X - 7) * (X - 1)    multiplying both sides by  removes the sqrt"

Starting from the original equation, if you move the lone X on the left to the right, you get sqrt(x-1) = x-7.  Squaring this gives us   x-1= (x-7)*(x-7).
Bear in mind that you can only solve quadratic equations when they are in the form: 0 = (x + A)*(x + B)
The left side must equal zero in order to isolate either (x + A) or (x + B) and solve for the answers.

Answer should be 10 in the end.

Dragunityking1 Featured By Owner Jul 30, 2014
So... much... MATHEMATICS!
fotland42 Featured By Owner Jul 24, 2014
It was too much bother to actually do the algebra, so I just assumed that the answer was probably 10 and confirmed.

I mean, it's probably a rational number between 0 and 10, which immediately narrows it down to 1, 2, 5, or 10.
e-tec Featured By Owner Jul 24, 2014  Hobbyist General Artist
PrincessCrystalSnow Featured By Owner Jul 21, 2014
Lyra is awsome
1cosmiconsciousness Featured By Owner Jul 17, 2014
Lyra is cool.
1cosmiconsciousness Featured By Owner Jul 3, 2014
I would've given that performance a 2x+(sq root of x)=3x-6
(how do I insert that symbol of square root?)
Speedy526745 Featured By Owner Aug 24, 2014  Hobbyist Digital Artist
I accept your challenge!

2x + sqrt(x) = 3x - 6
sqrt(x) = x - 6
x = (x - 6)2 = x2 - 12x + 36
0 = x2 - 13x + 36
0 = (x - 4)(x - 9)
10 ≠ 6, so x ≠ 4
21 = 21, so x = 9'd give it a 9?  Seriously?  What kept it from getting a sqrt[20*(sqrt(25))]? 
1cosmiconsciousness Featured By Owner Aug 25, 2014
First, that is very high. Second, it seemed that they were at a serious risk. Third, at the end, it seemed highly unlikely that they could be standing on one hoof on water, while holding a filly.
Besides, this comic deserves a (2*sqrt(5))sq *(sqrt4) out of sqrt100.
Speedy526745 Featured By Owner Aug 25, 2014  Hobbyist Digital Artist
You like doing this, don't you?

.....a 40 out of 10?!

......I'm ok with this.
1cosmiconsciousness Featured By Owner Jun 29, 2014
Gotta start givng out ratings that way. XD. Mess with so many people Troll!!! 
1cosmiconsciousness Featured By Owner Jun 29, 2014
Wow! A perfect 10!
Lol, the Doctor's face.
Yes, I worked it out. x=10
OtakuDanny Featured By Owner Jun 23, 2014  Hobbyist Artist
O_O How does she do that?
RedGryph0n Featured By Owner Jun 22, 2014  Hobbyist Digital Artist
XD 10
awesometroll-plz Featured By Owner Jun 10, 2014
W0nderbolts Featured By Owner Jun 8, 2014
Dudette5030 Featured By Owner May 28, 2014  Student General Artist
You know you're a math person when the first thing you do when you see this is try to find a pencil and some paper so you can solve this XD
(I got 10, so I guess that's the right answer :))
1cosmiconsciousness Featured By Owner Jun 29, 2014
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