anonymous
  • anonymous
Solve the quadratic equation by completing the square. x^2-12x+7=0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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SolomonZelman
  • SolomonZelman
add 29 to both sides.
SolomonZelman
  • SolomonZelman
can you add 29 to both sides?
anonymous
  • anonymous
which sides?

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More answers

SolomonZelman
  • SolomonZelman
Both. \[x^2-12+7+29=0+29\]
anonymous
  • anonymous
and why 29?
SolomonZelman
  • SolomonZelman
To make the left side into perfect square because you have to have (-6) (-6) which equals 36.
Hero
  • Hero
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 Take square root of both sides to finish solving for x
anonymous
  • anonymous
Oh. Okay. I still don't quite get it, but lets move on. What shall I do next? :D
anonymous
  • anonymous
Uhh... which one is right?
gorv
  • gorv
x^2-2*x*6+7=0 x^2-2*x*6+36-36+7=0 (x^2-2*x*6+36)-29=0 (x-6)^2-29=0 (x-6)^2=29 x-6=29^1/2 x=(29)^1/2+6
anonymous
  • anonymous
Are all of these right, just in different ways?
Hero
  • Hero
You add 36 to both sides, not 29
Hero
  • Hero
But 36 - 7 = 29
SolomonZelman
  • SolomonZelman
@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.
anonymous
  • anonymous
I'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
  • Hero
@SolomanZelman, if that's true, then explain how I got my result
gorv
  • gorv
actually 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
  • Hero
I know exactly how the process works and what to add to both sides.
SolomonZelman
  • SolomonZelman
@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
  • gorv
@hero if u will add 29 both side than on x^2-12x+7+29=29 x^2-12x+36=29
Hero
  • Hero
She'll only understand if those teaching know what they are talking about
SolomonZelman
  • SolomonZelman
STOP ARGUING!
SolomonZelman
  • SolomonZelman
YES, add 29
gorv
  • gorv
@hero plzz plzzzz plzzzz for god sake use little of ur mind
SolomonZelman
  • SolomonZelman
@Emily778, do you get how I came up with 29? Do you want to learn how to complete the square?
Hero
  • Hero
I think @Emily778 already has it figured out lol
SolomonZelman
  • SolomonZelman
MODERATOR, please don't ruin the thread, and confuse teh asker, lets teach her!
anonymous
  • anonymous
@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
  • SolomonZelman
Sorry If I was offensive, @Hero .
Hero
  • Hero
Finish solving for x @Emily778
Hero
  • Hero
Take the square root of both sides
anonymous
  • anonymous
Can you show me how? I am so confused:(
SolomonZelman
  • SolomonZelman
@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
  • SolomonZelman
to make the left side...typo
Hero
  • Hero
|dw:1384666594334:dw|
SolomonZelman
  • SolomonZelman
Emily, do you get it conceptually?
Hero
  • Hero
Add 6 to both sides to finish solving for x
anonymous
  • anonymous
yep.
anonymous
  • anonymous
so, like this @Hero (x-6)^2+6=29+6?
Hero
  • Hero
@Emily778, please observe what I did above first
Hero
  • Hero
I think you missed that last bit I posted in a drawing
anonymous
  • anonymous
oh, you have to square root first?
Hero
  • Hero
Yes you can't do anything until you take the square root of both sides.
Hero
  • Hero
@SolomonZelman, I assure you that we're supposed to add 36 to both sides. I wouldn't tell you anything wrong here.
Hero
  • Hero
If you don't believe me, I have ways of convincing you.
Hero
  • Hero
For one, I know you would never argue with WolframAlpha.
SolomonZelman
  • SolomonZelman
Hero, how does 36 make the left side into a perfect square, it is \[x^2+12x+7=0\]
Hero
  • Hero
Hang on, @SolomonZelman, WolframAlpha is undefeated.
SolomonZelman
  • SolomonZelman
I meant\[x^2-12x+7=0\]
anonymous
  • anonymous
okay, so it's actually x-6+6=+=sqrt29=6?
SolomonZelman
  • SolomonZelman
Well yes it is then.
nincompoop
  • nincompoop
omg don't argue with @Hero
SolomonZelman
  • SolomonZelman
@Hero, I am sorry to say this, but you have to rvw over some staff.
nincompoop
  • nincompoop
he is correct and I am telling you it
anonymous
  • anonymous
@hero okay, so it's actually x-6+6=+=sqrt29=6?
nincompoop
  • nincompoop
NOOOOOOOOOOOOOOO
Hero
  • Hero
http://tr.im/4klyc
SolomonZelman
  • SolomonZelman
Do 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
  • SolomonZelman
Don't tell me 1+1=4
nincompoop
  • nincompoop
I know I do not need a calculator and I know he is correct
Hero
  • Hero
Notice that wolframalpha says to add 36 to both sides.
Hero
  • Hero
In this here link: http://tr.im/4klyc
SolomonZelman
  • SolomonZelman
maybe you put in -7, instead of +7.
SolomonZelman
  • SolomonZelman
OK, when you subtract 7, but you can just add 29, without subtracting 7.
SolomonZelman
  • SolomonZelman
See?
anonymous
  • anonymous
Thankyou! Is that it @Hero
Hero
  • Hero
There's only one correct way to do it @SolomonZelman. Wolframalpha shows the steps. Go review them.
Hero
  • Hero
@Emily778, I think you have it but review your symbology for mistakes and check the link on WolframAlpha
SolomonZelman
  • SolomonZelman
@Hero it wastes a step on subtracting 7 from both sides, you still get the same thing, \[x^2-12+36=29\] Do you see my point?
anonymous
  • anonymous
okay
SolomonZelman
  • SolomonZelman
Do you guys just argue, or actually READ MY REPLIES?
nincompoop
  • nincompoop
solomon, study more before you question
SolomonZelman
  • SolomonZelman
@nincompoop, you obviously didn't understand what i said.
nincompoop
  • nincompoop
just study
SolomonZelman
  • SolomonZelman
Do you understand what I said, I don't need to study, I am fine.
nincompoop
  • nincompoop
study
Hero
  • Hero
@SolomonZelman, there's a difference between wasting steps and skipping steps.
Hero
  • Hero
Skipping steps leads to confusion
SolomonZelman
  • SolomonZelman
I 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
  • SolomonZelman
I still think though, that emily didn't get it conceptually.
nincompoop
  • nincompoop
she never does...
SolomonZelman
  • SolomonZelman
That was quite offensive.
Hero
  • Hero
Yes, but some things can be figured out through self-study, observation and understanding. One thing is for sure. She surely won't get it if she is fed incorrect info.
SolomonZelman
  • SolomonZelman
True, and I was trying to ask emily if she figured out the first step(s) in completing the square.
nincompoop
  • nincompoop
doubt it
SolomonZelman
  • SolomonZelman
Yes, me too, that's why I kept on asking that.
Hero
  • Hero
By 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.
nincompoop
  • nincompoop
couldn't agree more
SolomonZelman
  • SolomonZelman
Well, not that they taught me that, but didn't get any points off.
nincompoop
  • nincompoop
it's cool can't teach someone about skipping when that person barely knows anything to begin with
SolomonZelman
  • SolomonZelman
I don't really see the difference between subtracting seven at first or not. To me it makes perfect sense to do my way.
SolomonZelman
  • SolomonZelman
I see your point though....
nincompoop
  • nincompoop
1+1 = 4 though
SolomonZelman
  • SolomonZelman
And she still hasn't figure it out conceptually, just got the answer and left.
SolomonZelman
  • SolomonZelman
@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
  • nincompoop
it's called precision
SolomonZelman
  • SolomonZelman
\(\huge {\color{green} {Yup,} }\) forgot the name for this, I learned that last year.
nincompoop
  • nincompoop
anyway, good night
SolomonZelman
  • SolomonZelman
you too!
SolomonZelman
  • SolomonZelman
\(\huge {\color{green} {H} }\)\(\huge {\color{blue} {a} }\)\(\huge {\color{red} {v} }\)\(\huge {\color{orange} {e} }\) \(\huge {\color{purple} {a} }\) \(\huge {\color{lightblue} {n} }\)\(\huge {\color{grey} {i} }\)\(\huge {\color{brown} {g} }\)\(\huge {\color{lightgreen} {h} }\)\(\huge {\color{yellow }{t} }\)\(\huge {\color{darkgreen } {!} }\)
Hero
  • Hero
The difference between the methods is, one is systematic, and the other is not. The non-systematic method is an approach that some would refer to as improper methodology.
SolomonZelman
  • SolomonZelman
\[\(\huge {\color{green} {B^{Y^{E ^{!}}}} }\)\]
SolomonZelman
  • SolomonZelman
Didn't delete the parenthesis....
Hero
  • Hero
The 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
  • Hero
This is a systematic approach and you end up with (x + b/2)^2 = b^2/4 + c
SolomonZelman
  • SolomonZelman
Well, then improper methodology just shows that the person who did the steps is SMART.
Hero
  • Hero
Now let's see @SolomonZelman explain his method in a systematic, generalized manner.
SolomonZelman
  • SolomonZelman
I would just use an example similar to the one we solved just now.
Hero
  • Hero
Examples are not generalized. And they don't show the systematic methodology.
Hero
  • Hero
Systematic methods have a better chance of being understood than non-systematic methods.
SolomonZelman
  • SolomonZelman
OK, 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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