What is a quadratic polynomial?

I completed the square for the following equation. I am attaching my work here on pen and paper. I typed it though so future visitors may understand it clearly.
x^2 + 12x + 32= 0 this is a classic according to the book.
 
it is not letting me attach it. Neither word doc or pdf. I took pics and send it to my email and let's see if I get them so I can download them and attach them here.
 
eddy2017 said:
Even if I have to pay for it. Send it to me and tell me how much it cost
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I don't use the forum for anything that involves sending or receiving money. We provide free math help.

eddy2017 said:
I sent you a PM about an equation solver you offered to send me
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Yes you did, and I forgot to reply to that message. However, I had replied in our original conversation: I'm still waiting for you to finish what you'd started. Instead of bringing that conversation into this thread, I would prefer to continue that discussion using the original conversation. I'd like you to re-read the entire conversation, too. I think you've forgotten some of what we'd talked about.

eddy2017 said:
You talked about how simple and effective [the program is] and how good it managed the grouping symbols.
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You'll need to point out where I'd said those things because I recall something different. The software doesn't "manage" grouping symbols. You need to do that. The software provides error messages regarding mismatched grouping symbols, and I'd said that I would use it to check the grouping symbols (line by line) in your work. You could use it for that same purpose. I could show you also how to use it for checking your algebra. Doing so would force you to practice typing grouping symbols. Alternatively, you could paste your typed expressions into wolframalpha, as I'd shown you. Wolframalpha now parses grouping symbols in real time, using color coding to indicate both mismatches and properly-closed groupings. After you enter your expression, wolframalpha also displays your input formatted, so you can see how your typing has been interpreted.

?
 
well, i typed it all in a word document. can i attach the pictures I took?
 
mmm4444bot said:
Is there something preventing you from typing your expressions/equations directly into a post?

?
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NO, nothing, i just had typed everything on a word document. I took pics and want to ask if I can paste them all here. It will take me work and time.
 
mmm4444bot said:
I don't use the forum for anything that involves sending or receiving money. We provide free math help.


Yes you did, and I forgot to reply to that message. However, I had replied in our original conversation: I'm still waiting for you to finish what you'd started. Instead of bringing that conversation into this thread, I would prefer to continue that discussion using the original conversation. I'd like you to re-read the entire conversation, too. I think you've forgotten some of what we'd talked about.


You'll need to point out where I'd said those things because I recall something different. The software doesn't "manage" grouping symbols. You need to do that. The software provides error messages regarding mismatched grouping symbols, and I'd said that I would use it to check the grouping symbols (line by line) in your work. You could use it for that same purpose. I could show you also how to use it for checking your algebra. Doing so would force you to practice typing grouping symbols. Alternatively, you could paste your typed expressions into wolframalpha, as I'd shown you. Wolframalpha now parses grouping symbols in real time, using color coding to indicate both mismatches and properly-closed groupings. After you enter your expression, wolframalpha also displays your input formatted, so you can see how your typing has been interpreted.

?
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Yes, you are right. I remember now. I did not recall our conversation entirely. I know you don't use it to make money. it is only that I remembered you offering that software to me and then I could not keep up at the moment with your teaching because I was still holding down two jobs.
 
eddy2017 said:
Yes, you are right. I remember now. I did not recall our conversation entirely. I know you don't use it to make money. it is only that I remembered you offering that software to me and then I could not keep up at the moment with your teaching because I was still holding down two jobs.
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but if you do not want to send it is okay, mmm. I appreciate your help, man.
 
mmm4444bot said:
I don't use the forum for anything that involves sending or receiving money. We provide free math help.


Yes you did, and I forgot to reply to that message. However, I had replied in our original conversation: I'm still waiting for you to finish what you'd started. Instead of bringing that conversation into this thread, I would prefer to continue that discussion using the original conversation. I'd like you to re-read the entire conversation, too. I think you've forgotten some of what we'd talked about.


You'll need to point out where I'd said those things because I recall something different. The software doesn't "manage" grouping symbols. You need to do that. The software provides error messages regarding mismatched grouping symbols, and I'd said that I would use it to check the grouping symbols (line by line) in your work. You could use it for that same purpose. I could show you also how to use it for checking your algebra. Doing so would force you to practice typing grouping symbols. Alternatively, you could paste your typed expressions into wolframalpha, as I'd shown you. Wolframalpha now parses grouping symbols in real time, using color coding to indicate both mismatches and properly-closed groupings. After you enter your expression, wolframalpha also displays your input formatted, so you can see how your typing has been interpreted.

?
Click to expand...
Yes you did, and I forgot to reply to that message. However, I had replied in our original conversation: I'm still waiting for you to finish what you'd started. Instead of bringing that conversation into this thread, I would prefer to continue that discussion using the original conversation. I'd like you to re-read the entire conversation, too. I think you've forgotten some of what we'd talked about.

what was that?.
Oh, i went back to our conversation and read it. Ok, sorry, I am gonna send you a pm, ok. If i ask you here it was because you were not answering.
 
Complete the square

X^2 + 12x + 32=0

Step 1

TAKE EVERYTHING THAT HAS AN X TERM IN IT AND PUT IT ON ONE SIDE OF THE EQUAL SIGN ( the rest goes on the other side of the equal sign)

So, this means that 32 needs to go to the other side, and we do that subtracting 32 from both sides

x^2 + 12x + 32-32 =0-32

x^2 + 12x =-32

step 2

put the left hand side into this form:

x^2 + 12x + ___ (some number)= -32

we don’t know what the number is, but our goal is try to make this into a perfect square.

Step 3

Determine what that unknow value is (let’s call it c value)

Whatever it is we need to find a number that when we add it to itself we get 12 and when we multiply it by itself we get the missing number for the blank space, so,

We need to complete the square and here’s a way to that,

Take the b value in our expression= 12 and divide it by 2 = 6

Now, take 6 and square it =6^2= 36

Then, 36 is our c value, the value that goes in the blank,

x^2 + 12x + ___=-32

x^2 + 12x + 36= so this is what we call a perfect square,

but since we added 36 to the left hand side we need to do the same to the right hand side

x^2 + 12x + 36 =-32+36 (this will reduce to 4 on the rhs)

x^2 + 12x + 36 =4

step 4

now that we have this trinomial on the left, let’s factor it

remember that this should be a perfect square.

x^2 + 12x + 36 =4

now that we have this trinomial on the left, let’s factor it.

when we factor it, we get,

(x+6)(x+6)= 4 recuerda que 6 porque es la mitad del valor b(segundo termino).

It is a perfect square cos we have two identical binomials being multiplied together,

And notice the value of 6, what happens when we add it to itself? We get 12

And when we multiply it together we get 36.

So, (x+6)+(x+6)=4

(x+6)^2 = 4

And now that we have it on this form we are ready to solve for x

To solve this equation for x, we need to remove the square.


Step 5

We need to take the square of both sides, so,

√(x+6)^2= √4

x+6= ±2

now,we have a positive and a negative value for 2.

Step 6

Let’s split these two values into two different problems and solve them.

X+6 =+2 and x+6= -2

Let’s solve for x in both problems and we get two different answers

X=-4 and x=-8

And now we have our answers. X is -4 and x is -8

If you take either one of these values and plug them into the original equation the left hand side should equal 0.

Let’s check our answer.

Let’s plug -4 and see if we get 0

X^2 + 12x + 32=0

(-4)^2 + 12(-4)+32= 0

This reduces to,

16-48+32=0

The left hand side reduces to 0 and we are left with

0=0 we get a value that equals 0 so that means that -4 is one of our answers

Now let’s do the same thing with our other value, -8

X^2 + 12x + 32=0

(-8)^2+12(-8)+32=0

Simplifyin’ we have

64-96+32=0

Left side reduces to 0

Making our value of -8 a true one.
 
These are the steps to follow to complete the square in an equation like that. At least, that is the way i have seen it as i have studied this for some time since i started the thread.
 
eddy2017 said:
can i attach the pictures I took?
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I don't understand why you've asked that. We already know you can post pictures. You've done it before.

Or, are you thinking that you need permission this time?

You don't need to ask permission before uploading math images. However, keep in mind that tutors cannot quote expressions from images. We prefer that algebra students learn to type math expressions using grouping symbols, just like what they need to do when using technology.

[imath]\;[/imath]
 
mmm4444bot said:
I don't understand why you've asked that. We already know you can post pictures. You've done it before.

Or, are you thinking that you need permission this time?

You don't need to ask permission before uploading math images. However, keep in mind that tutors cannot quote expressions from images. We prefer that algebra students learn to type math expressions using grouping symbols, just like what they need to do when using technology.

[imath]\;[/imath]
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I was thinking I needed permission to do that because I was banned and I have been allowed back into the forum which I love so much. I have to be very careful on what I do. so if in doubt I better ask. Thank you. I know now I can upload pics again. I pmed you.
 
Yes, I am trying to type everything in here but, as I know you know, some expressions are difficult to type in clearly without la text and I have been advised by tutors not to devote time now to learning la tex which I know they do because they want me to focus on everything math.
 
eddy2017 said:
mmm4444bot said:
I think you've forgotten some of what we'd talked about.
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what was that?
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Most of what we'd discussed about grouping symbols. For example, in this thread, you'd posted that you were "amazed" at how the meaning of an expression changes when grouping symbols are missing. But, we'd just covered that very topic. In fact, several people have tutored you about grouping symbols in this forum (for years). Yet, you continue starting threads without required grouping symbols. So, either you never understood to begin with (despite your repeated claims to the contrary) or you keep forgetting. Personally, I think you tend to forget things because you don't give your brain a chance to encode the patterns. You seem to jump from topic to topic, without sufficient practice before moving on.

If i ask you here it was because you were not answering.
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But, I had answered. Regardless, my point is that you don't need to continue previous discussions by raising them in separate threads. If you feel that something has been missed, inquire at the source. Many of your threads become somewhat unwieldy because they're not focused. Sometimes, your threads end up like multiple daydreams strung together, with no clear train of thought.

;)
 
eddy2017 said:
I was thinking I needed permission to do that because I was banned
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That doesn't make any sense, Eddy. You were banned two days specifically for problematic behavior (not for posting images). Also, you have posted many images since then. Why the big concern about posting images today?

:confused:
 
mmm4444bot said:
Most of what we'd discussed about grouping symbols. For example, in this thread, you'd posted that you were "amazed" at how the meaning of an expression changes when grouping symbols are missing. But, we'd just covered that very topic. In fact, several people have tutored you about grouping symbols in this forum (for years). Yet, you continue starting threads without required grouping symbols. So, either you never understood to begin with (despite repeated claims to the contrary) or you keep forgetting. Personally, I think you tend to forget things because you don't give your brain a chance to encode the patterns. You seem to jump from topic to topic, without sufficient practice before moving on.


But, I had answered. Regardless, my point is that you don't need to continue previous discussions by raising them in separate threads. If you feel that something has been missed, inquire at the source. Many of your threads become somewhat unwieldy because they're not focused. Sometimes, your threads end up like multiple daydreams strung together, with no clear train of thought.

;)
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Hey, mmm, you told me not to post in other people's threads!. You asked me to open another thread and quote the other. So, what should I do then. A few minutes ago i had a doubt about something posted here in pre-algebra and following your advice i opened another thread to ask about my doubt. Following what you yourself told me.:unsure:
 
Okay, mmm, excuse my ramblings, then. I appreciate you a lot. thank you!!. I will try to keep from posting. I have to study a lot, anyways. I will continue in the forum if you do not mind though.
 
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