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Emily778
 2 years ago
Solve the quadratic equation by completing the square.
x^212x+7=0
Emily778
 2 years ago
Solve the quadratic equation by completing the square. x^212x+7=0

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SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1add 29 to both sides.

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1can you add 29 to both sides?

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1Both. \[x^212+7+29=0+29\]

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1To make the left side into perfect square because you have to have (6) (6) which equals 36.

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1x^2  12x + 7 = 0 x^2  12x = 7 x^2  12x + (12/2)^2 = (12/2)^2  7 x^2  12x + 36 = 36  7 (x  6)^2 = 29 Take square root of both sides to finish solving for x

Emily778
 2 years ago
Best ResponseYou've already chosen the best response.1Oh. Okay. I still don't quite get it, but lets move on. What shall I do next? :D

Emily778
 2 years ago
Best ResponseYou've already chosen the best response.1Uhh... which one is right?

gorv
 2 years ago
Best ResponseYou've already chosen the best response.2x^22*x*6+7=0 x^22*x*6+3636+7=0 (x^22*x*6+36)29=0 (x6)^229=0 (x6)^2=29 x6=29^1/2 x=(29)^1/2+6

Emily778
 2 years ago
Best ResponseYou've already chosen the best response.1Are all of these right, just in different ways?

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1You add 36 to both sides, not 29

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1@Hero, no you add 29, because that makes the left side into perfect square. @Emily778, I know what you are confused about, lets learn how to complete the square.

Emily778
 2 years ago
Best ResponseYou've already chosen the best response.1I'll just do this x^2  12x + 7 = 0 x^2  12x = 7 x^2  12x + (12/2)^2 = (12/2)^2  7 x^2  12x + 36 = 36  7 (x  6)^2 = 29

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1@SolomanZelman, if that's true, then explain how I got my result

gorv
 2 years ago
Best ResponseYou've already chosen the best response.2actually in (a+b)^2=a^2+b^2+2ab here 2ab is 12x=2*x*6 so u need to make b^2 that is 36

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1I know exactly how the process works and what to add to both sides.

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1@Emily778, do you get how I came up with 29? lets do a different example. GUYS PLEASE, LETS TEACH HER, NOT DO HER WORK> She needs to understand.

gorv
 2 years ago
Best ResponseYou've already chosen the best response.2@hero if u will add 29 both side than on x^212x+7+29=29 x^212x+36=29

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1She'll only understand if those teaching know what they are talking about

gorv
 2 years ago
Best ResponseYou've already chosen the best response.2@hero plzz plzzzz plzzzz for god sake use little of ur mind

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1@Emily778, do you get how I came up with 29? Do you want to learn how to complete the square?

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1I think @Emily778 already has it figured out lol

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1MODERATOR, please don't ruin the thread, and confuse teh asker, lets teach her!

Emily778
 2 years ago
Best ResponseYou've already chosen the best response.1@Hero What do I do after this? Or is it already done? x^2  12x + 7 = 0 x^2  12x = 7 x^2  12x + (12/2)^2 = (12/2)^2  7 x^2  12x + 36 = 36  7 (x  6)^2 = 29

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1Sorry If I was offensive, @Hero .

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1Finish solving for x @Emily778

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1Take the square root of both sides

Emily778
 2 years ago
Best ResponseYou've already chosen the best response.1Can you show me how? I am so confused:(

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1@Emily778 PLEASE read this CAREFULLY. Do you know how to come up with the number that you have to add to both sides to ake the left side into a perfect square?

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1to make the left side...typo

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1Emily, do you get it conceptually?

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1Add 6 to both sides to finish solving for x

Emily778
 2 years ago
Best ResponseYou've already chosen the best response.1so, like this @Hero (x6)^2+6=29+6?

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1@Emily778, please observe what I did above first

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1I think you missed that last bit I posted in a drawing

Emily778
 2 years ago
Best ResponseYou've already chosen the best response.1oh, you have to square root first?

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1Yes you can't do anything until you take the square root of both sides.

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1@SolomonZelman, I assure you that we're supposed to add 36 to both sides. I wouldn't tell you anything wrong here.

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1If you don't believe me, I have ways of convincing you.

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1For one, I know you would never argue with WolframAlpha.

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1Hero, how does 36 make the left side into a perfect square, it is \[x^2+12x+7=0\]

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1Hang on, @SolomonZelman, WolframAlpha is undefeated.

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1I meant\[x^212x+7=0\]

Emily778
 2 years ago
Best ResponseYou've already chosen the best response.1okay, so it's actually x6+6=+=sqrt29=6?

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1Well yes it is then.

nincompoop
 2 years ago
Best ResponseYou've already chosen the best response.1omg don't argue with @Hero

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1@Hero, I am sorry to say this, but you have to rvw over some staff.

nincompoop
 2 years ago
Best ResponseYou've already chosen the best response.1he is correct and I am telling you it

Emily778
 2 years ago
Best ResponseYou've already chosen the best response.1@hero okay, so it's actually x6+6=+=sqrt29=6?

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1Do you guys know how to complete the square, you don't need any online calculator for this. Idk how to even tell you this. you help with hard staff that I have no clue about, and make a simple error, in completing a square.

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1Don't tell me 1+1=4

nincompoop
 2 years ago
Best ResponseYou've already chosen the best response.1I know I do not need a calculator and I know he is correct

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1Notice that wolframalpha says to add 36 to both sides.

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1In this here link: http://tr.im/4klyc

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1maybe you put in 7, instead of +7.

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1OK, when you subtract 7, but you can just add 29, without subtracting 7.

Emily778
 2 years ago
Best ResponseYou've already chosen the best response.1Thankyou! Is that it @Hero

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1There's only one correct way to do it @SolomonZelman. Wolframalpha shows the steps. Go review them.

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1@Emily778, I think you have it but review your symbology for mistakes and check the link on WolframAlpha

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1@Hero it wastes a step on subtracting 7 from both sides, you still get the same thing, \[x^212+36=29\] Do you see my point?

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1Do you guys just argue, or actually READ MY REPLIES?

nincompoop
 2 years ago
Best ResponseYou've already chosen the best response.1solomon, study more before you question

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1@nincompoop, you obviously didn't understand what i said.

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1Do you understand what I said, I don't need to study, I am fine.

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1@SolomonZelman, there's a difference between wasting steps and skipping steps.

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1Skipping steps leads to confusion

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1I am not saying the Wolframalpha is wrong, it just has a different way of showing... Yes, my bad, perhaps I skipped it, not wasted.... My teacher told me that both ways are valid, and to me that makes perfect sense. And YES, instead of arguing lets continue studying.

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1I still think though, that emily didn't get it conceptually.

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1That was quite offensive.

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1Yes, but some things can be figured out through selfstudy, observation and understanding. One thing is for sure. She surely won't get it if she is fed incorrect info.

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1True, and I was trying to ask emily if she figured out the first step(s) in completing the square.

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1Yes, me too, that's why I kept on asking that.

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1By the way @SolomonZelman, I'm fully aware of your method of doing it. But I abandoned it after I realized that steps were being skipped. It is wrong for teachers to teach it that way.

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1Well, not that they taught me that, but didn't get any points off.

nincompoop
 2 years ago
Best ResponseYou've already chosen the best response.1it's cool can't teach someone about skipping when that person barely knows anything to begin with

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1I don't really see the difference between subtracting seven at first or not. To me it makes perfect sense to do my way.

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1I see your point though....

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1And she still hasn't figure it out conceptually, just got the answer and left.

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1@nincompoop, actually in biology that could be true, like when parents (or future parents) combine or whatever the word for that is... LIKE twins.

nincompoop
 2 years ago
Best ResponseYou've already chosen the best response.1it's called precision

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1\(\huge {\color{green} {Yup,} }\) forgot the name for this, I learned that last year.

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1\(\huge {\color{green} {H} }\)\(\huge {\color{blue} {a} }\)\(\huge {\color{red} {v} }\)\(\huge {\color{orange} {e} }\) \(\huge {\color{purple} {a} }\) \(\huge {\color{lightblue} {n} }\)\(\huge {\color{grey} {i} }\)\(\huge {\color{brown} {g} }\)\(\huge {\color{lightgreen} {h} }\)\(\huge {\color{yellow }{t} }\)\(\huge {\color{darkgreen } {!} }\)

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1The difference between the methods is, one is systematic, and the other is not. The nonsystematic method is an approach that some would refer to as improper methodology.

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1\[\(\huge {\color{green} {B^{Y^{E ^{!}}}} }\)\]

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1Didn't delete the parenthesis....

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1The method I use can be generalized to this: You begin with x^2 + bx  c = 0 add c to both sides: x^2 + bx = c Then add (b/2)^2 to both sides: x^2 + bx + (b/2)^2 = (b/2)^2 + c

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1This is a systematic approach and you end up with (x + b/2)^2 = b^2/4 + c

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1Well, then improper methodology just shows that the person who did the steps is SMART.

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1Now let's see @SolomonZelman explain his method in a systematic, generalized manner.

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1I would just use an example similar to the one we solved just now.

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1Examples are not generalized. And they don't show the systematic methodology.

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1Systematic methods have a better chance of being understood than nonsystematic methods.

SolomonZelman
 2 years ago
Best ResponseYou've already chosen the best response.1OK, I already said that I agree that to start teaching, systematic.... but not using it still shows that the solver is smarter.
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