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January 8th, 2014, 09:28 AM   #1
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Completing the Square question.

Hi, I'm currently learning about quadratic equations and 'Completing the Square'. Basically, I need to know what I am doing it correct.

I have this equation:

x^2 + 5x + 2 = 0


I have worked out that (be it correct or incorrect) that:

x = 3.207 or x = 1.792


But when I input one of these numbers into the equation, I don't get an answer that is zero.

Have I answered this question correctly? And if so, how can I check I have? If not, what have I done wrong?

I can take a photo of my workings out and post them if needs be.


Many Thanks
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January 8th, 2014, 09:58 AM   #2
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Re: Completing the Square question.

Quote:
Originally Posted by GuyDoingMathFoiled
Have I answered this question correctly?
The equation has two negative roots as easily as can be seen by rule of signs, so definitely no.
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January 8th, 2014, 10:01 AM   #3
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Re: Completing the Square question.

Hello, GuyDoingMathFoiled!

Quote:


I have worked out that (be it correct or incorrect) that:[color=beige] .[/color]

But when I input one of these numbers into the equation, I don't get an answer that is zero.

What have I done wrong?

It's hard to see your work from here,
but it looks like you played the instead of the











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January 9th, 2014, 07:05 AM   #4
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Re: Completing the Square question.

I don't understand what I'm doing wrong here. I feel so dumb. Here is another equation I've got which for some reason I'm doing wrong. I'll type out my workings out in a hope someone will be able to point me in the right direction. (I don't know how to use the proper mathematical symbols on this forum so bear with me).

x^2 -3x - 4 = 0

x^2 -3x = 4

x^2 -3x -(3/2)^2 = 4 -(3/2)^2

(x - 3/2)^2 = 7/4

x - 3/2 = ?7/4

x = -3/2 ?7/4

x = -0.177 or -2.823


If the above is too messy to read, please point me towards a site I can convert it into mathematic expressions.

Thanks for the help!
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January 9th, 2014, 07:49 AM   #5
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Re: Completing the Square question.

In line 3, try adding (3/2)^2 instead of subtracting it.
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January 9th, 2014, 08:15 AM   #6
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Re: Completing the Square question.

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Originally Posted by greg1313
In line 3, try adding (3/2)^2 instead of subtracting it.
I thought it had to be -3/2, because to get it you have to divide the -3 by 2.
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January 9th, 2014, 08:19 AM   #7
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Re: Completing the Square question.

Quote:
Originally Posted by GuyDoingMathFoiled
I don't understand what I'm doing wrong here. I feel so dumb. Here is another equation I've got which for some reason I'm doing wrong. I'll type out my workings out in a hope someone will be able to point me in the right direction. (I don't know how to use the proper mathematical symbols on this forum so bear with me).
I think what might be misleading you a bit is line 3. You've got:



You can only subtract it from the LHS.



And then you can move it to the other side by adding it to both sides.



Personally, I prefer doing it this way than adding it to both sides. It's a question of preference I guess.

Had to edit that a couple of times to make it look correct!
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January 9th, 2014, 10:33 AM   #8
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Re: Completing the Square question.

Quote:
Originally Posted by Slinkey
Quote:
Originally Posted by GuyDoingMathFoiled
I don't understand what I'm doing wrong here. I feel so dumb. Here is another equation I've got which for some reason I'm doing wrong. I'll type out my workings out in a hope someone will be able to point me in the right direction. (I don't know how to use the proper mathematical symbols on this forum so bear with me).
I think what might be misleading you a bit is line 3. You've got:



You can only subtract it from the LHS.



And then you can move it to the other side by adding it to both sides.



Personally, I prefer doing it this way than adding it to both sides. It's a question of preference I guess.

Had to edit that a couple of times to make it look correct!

Okay, but (and I'm not disputing what you say, just asking to understand better), here:



You subtract from the left hand side, to make the equation equal, do you not also need to subtract from the right hand side?
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January 9th, 2014, 11:12 AM   #9
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Re: Completing the Square question.







See?
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January 9th, 2014, 12:26 PM   #10
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Re: Completing the Square question.

Quote:
Originally Posted by GuyDoingMathFoiled
Okay, but (and I'm not disputing what you say, just asking to understand better), here:



You subtract from the left hand side, to make the equation equal, do you not also need to subtract from the right hand side?
Sure, and I am glad that you want to understand. That is the sign of a good student!!

OK, let's just look at the LHS here OK?

We started with



When we square it we get



Let's take the first term here:



and expand it.



Notice that we have 9/4 too much!!!

That's why we have to subtract it.

Hence:



That is why you don't put it on the RHS of the equation as well. The equation is still balanced.

Hope that helps.
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