# How would you solve the equation 2+2X2?
**URL:** https://boards.straightdope.com/t/how-would-you-solve-the-equation-2-2x2/582144
**Category:** Factual Questions
**Created:** [May 16, 2011, 10:00pm UTC](https://boards.straightdope.com/t/how-would-you-solve-the-equation-2-2x2/582144 "2011-05-16T22:00:43Z")
**Posts on this page:** 20
**Page:** 2
### Author:  [@what\_do\_I\_type\_here](https://boards.straightdope.com/u/what_do_I_type_here)
#### Post date: [May 17, 2011, 5:15pm UTC](https://boards.straightdope.com/t/how-would-you-solve-the-equation-2-2x2/582144/21 "2011-05-17T17:15:04Z")
It’s not an equation. Equations have equal signs.
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### Author:  [@John\_DiFool](https://boards.straightdope.com/u/John_DiFool)
#### Post date: [May 17, 2011, 5:35pm UTC](https://boards.straightdope.com/t/how-would-you-solve-the-equation-2-2x2/582144/22 "2011-05-17T17:35:38Z")
[Duplicate Post]
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### Author:  [@John\_DiFool](https://boards.straightdope.com/u/John_DiFool)
#### Post date: [May 17, 2011, 5:37pm UTC](https://boards.straightdope.com/t/how-would-you-solve-the-equation-2-2x2/582144/23 "2011-05-17T17:37:39Z")
> [@etv78](#):
>
> i fully expect this to become a pemdas trainwreck.
permdas.
Hmm for some strange reason this keeps reverting to all lower case-I just edited it twice and I know I put it in upper case. Anyway It Just Bugs Me that teachers leave out radicals (I always put them back in when I discuss OOP with my students).
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### Author:  [@President\_Johnny\_Gentle](https://boards.straightdope.com/u/President_Johnny_Gentle)
#### Post date: [May 17, 2011, 7:38pm UTC](https://boards.straightdope.com/t/how-would-you-solve-the-equation-2-2x2/582144/24 "2011-05-17T19:38:12Z")
> [@John\_DiFool](#):
>
> Anyway It Just Bugs Me that teachers leave out radicals (I always put them back in when I discuss OOP with my students).
No one’s leaving them out - a radical is an exponent, so is evaluated simultaneously.
My pet peeve with the acronym for OOP is that it makes it seem like all multiplication should be done before division and all addition before subtraction, which is untrue in the conventional ordering.
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### Author:  [@garygnu](https://boards.straightdope.com/u/garygnu)
#### Post date: [May 17, 2011, 8:28pm UTC](https://boards.straightdope.com/t/how-would-you-solve-the-equation-2-2x2/582144/25 "2011-05-17T20:28:47Z")
> [@President\_Johnny\_Gentle](#):
>
> …My pet peeve with the acronym for OOP is that it makes it seem like all multiplication should be done before division and all addition before subtraction, which is untrue in the conventional ordering.
Mnemonics are simple by definition. What would you have it be instead?
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### Author:  [@President\_Johnny\_Gentle](https://boards.straightdope.com/u/President_Johnny_Gentle)
#### Post date: [May 17, 2011, 8:34pm UTC](https://boards.straightdope.com/t/how-would-you-solve-the-equation-2-2x2/582144/26 "2011-05-17T20:34:41Z")
> [@garygnu](#):
>
> Mnemonics are simple by definition. What would you have it be instead?
The problem stems from the fact that the mnemonic is mistaught. The elementary teacher who taught me order of operations would have insisted that 8 - 4 + 4 = 0, which is not the way that it should be interpreted in the conventional order of operations.
Something like PEMA would be preferable, so long as care is taken to indicate that the M means both multiplication and division, since they are aspects of the same operation. Likewise for addition and subtraction.
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### Author:  [@Martin\_Hyde](https://boards.straightdope.com/u/Martin_Hyde)
#### Post date: [May 17, 2011, 10:33pm UTC](https://boards.straightdope.com/t/how-would-you-solve-the-equation-2-2x2/582144/27 "2011-05-17T22:33:49Z")
When I first saw this weird order of operations meme going around on the internet it was with the expression:
6 ÷ 2(1+2)
The wrong answer of the unsuspecting person is 1. The correct answer is 9.
The thing is, because of the way it is written / presented I can’t even “bemoan the state of maths education in this country” over people getting it wrong.
If it was written
6 ÷ 2 \* (1+2) I think far fewer people would get confused.
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### Author:  [@The\_Hamster\_King](https://boards.straightdope.com/u/The_Hamster_King)
#### Post date: [May 17, 2011, 11:35pm UTC](https://boards.straightdope.com/t/how-would-you-solve-the-equation-2-2x2/582144/28 "2011-05-17T23:35:59Z")
You mean “2 2 x 2 +” ?
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### Author:  [@Snarky\_Kong](https://boards.straightdope.com/u/Snarky_Kong)
#### Post date: [May 17, 2011, 11:43pm UTC](https://boards.straightdope.com/t/how-would-you-solve-the-equation-2-2x2/582144/29 "2011-05-17T23:43:05Z")
> [@Martin\_Hyde](#):
>
> When I first saw this weird order of operations meme going around on the internet it was with the expression:
>
> 6 ÷ 2(1+2)
>
> The wrong answer of the unsuspecting person is 1. The correct answer is 9.
>
> The thing is, because of the way it is written / presented I can’t even “bemoan the state of maths education in this country” over people getting it wrong.
>
> If it was written
>
> 6 ÷ 2 \* (1+2) I think far fewer people would get confused.
I think every mathematician in the GQ thread agreed that your first equation is ambiguous and not that there are right and wrong answers to it.
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### Author:  [@fluiddruid](https://boards.straightdope.com/u/fluiddruid)
#### Post date: [May 18, 2011, 7:12pm UTC](https://boards.straightdope.com/t/how-would-you-solve-the-equation-2-2x2/582144/30 "2011-05-18T19:12:11Z")
I’m not seeing a game here, so I’m moving this thread to GQ.
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### Author:  [@Hbns](https://boards.straightdope.com/u/Hbns)
#### Post date: [May 18, 2011, 7:50pm UTC](https://boards.straightdope.com/t/how-would-you-solve-the-equation-2-2x2/582144/31 "2011-05-18T19:50:38Z")
> [@fluiddruid](#):
>
> I’m not seeing a game here, so I’m moving this thread to GQ.
Had to try it with the Microsoft calculator in windows.
Microsoft calculator (standard) returns 8
Microsoft calculator (scientific) returns 6
No surprise I guess.
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### Author:  [@Hypnagogic\_Jerk](https://boards.straightdope.com/u/Hypnagogic_Jerk)
#### Post date: [May 18, 2011, 8:18pm UTC](https://boards.straightdope.com/t/how-would-you-solve-the-equation-2-2x2/582144/32 "2011-05-18T20:18:36Z")
> [@panamajack](#):
>
> It’s obvious to me. X has a root at -1/2.
Please. It’s clearly +/- i.
> [@Snarky\_Kong](#):
>
> I think every mathematician in the GQ thread agreed that your first equation is ambiguous and not that there are right and wrong answers to it.
I assume you’re referring to [thread=606537]this thread[/thread]. I’d encourage **Martin Hyde** or anyone else who’s interested to read it, as it does a good job at explaining where the ambiguity lies.
As for the expression in the OP of this thread, I think we’ve done a good job at showing that it can be construed as ambiguous as well. 😛 Though of course, if X refers to the multiplication operator, it’s definitely 6.
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### Author:  [@pulykamell](https://boards.straightdope.com/u/pulykamell)
#### Post date: [May 18, 2011, 8:40pm UTC](https://boards.straightdope.com/t/how-would-you-solve-the-equation-2-2x2/582144/33 "2011-05-18T20:40:39Z")
> [@what\_do\_I\_type\_here](#):
>
> It’s not an equation. Equations have equal signs.
This confused me, too. (And I wasn’t trying to be a pedantic prick. It took me a couple of posts to realize how people were coming up with an answer. I’m thinking, “how are you evaluating X=6” when there’s no other side to this equation.) For that matter, I still don’t quite understand how people are coming up with answers for X when there’s no other side to the equation.
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### Author:  [@Darth\_Panda](https://boards.straightdope.com/u/Darth_Panda)
#### Post date: [May 18, 2011, 8:45pm UTC](https://boards.straightdope.com/t/how-would-you-solve-the-equation-2-2x2/582144/34 "2011-05-18T20:45:34Z")
I’d use math.
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### Author:  [@President\_Johnny\_Gentle](https://boards.straightdope.com/u/President_Johnny_Gentle)
#### Post date: [May 18, 2011, 8:59pm UTC](https://boards.straightdope.com/t/how-would-you-solve-the-equation-2-2x2/582144/35 "2011-05-18T20:59:59Z")
> [@pulykamell](#):
>
> This confused me, too. (And I wasn’t trying to be a pedantic prick. It took me a couple of posts to realize how people were coming up with an answer. I’m thinking, “how are you evaluating X=6” when there’s no other side to this equation.) For that matter, I still don’t quite understand how people are coming up with answers for X when there’s no other side to the equation.
By setting the expression equal to 0, and solving for “X”.
The -1/2 answer interprets the expression as the equation 2 + 2_x_2 = 0 and the +/- i answer interprets it as 2+2\*x^2 = 0.
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### Author:  [@pulykamell](https://boards.straightdope.com/u/pulykamell)
#### Post date: [May 18, 2011, 9:28pm UTC](https://boards.straightdope.com/t/how-would-you-solve-the-equation-2-2x2/582144/36 "2011-05-18T21:28:31Z")
> [@President\_Johnny\_Gentle](#):
>
> By setting the expression equal to 0, and solving for “X”.
>
> The -1/2 answer interprets the expression as the equation 2 + 2_x_2 = 0 and the +/- i answer interprets it as 2+2\*x^2 = 0.
Is it typical to do that? I mean, would one normally write an equation omitting the “=0” part and be understood?
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### Author:  [@Chronos](https://boards.straightdope.com/u/Chronos)
#### Post date: [May 18, 2011, 9:31pm UTC](https://boards.straightdope.com/t/how-would-you-solve-the-equation-2-2x2/582144/37 "2011-05-18T21:31:33Z")
> [@](#):
>
> Is it typical to do that? I mean, would one normally write an equation omitting the “=0” part and be understood?
It depends on the context. One ordinarily refers to that as the root of the expression, not as the solution to the equation, but whatever you call it, it’s certainly something that’s done a fair amount.
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### Author:  [@pulykamell](https://boards.straightdope.com/u/pulykamell)
#### Post date: [May 18, 2011, 9:40pm UTC](https://boards.straightdope.com/t/how-would-you-solve-the-equation-2-2x2/582144/38 "2011-05-18T21:40:18Z")
OK, so I could say something like “what are the roots of x^2+5” and it won’t sound like half a sentence? Is this acceptable with linear equations, too? (i.e. do you call it a “root” too, and can you phrase is “what’s the root of x+5”?)
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### Author:  [@psychobunny](https://boards.straightdope.com/u/psychobunny)
#### Post date: [May 18, 2011, 9:52pm UTC](https://boards.straightdope.com/t/how-would-you-solve-the-equation-2-2x2/582144/39 "2011-05-18T21:52:03Z")
I didn’t know that multiplication takes precedence. I guess I learn something new every day. I would have answered either 8 or 6 depending on how you read it, but without parentheses, I would likely have gone right to left ie:
2+2x2=8
(2+2)x2=8
2+(2x2)=6
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### Author:  [@Deegeea](https://boards.straightdope.com/u/Deegeea)
#### Post date: [May 18, 2011, 9:53pm UTC](https://boards.straightdope.com/t/how-would-you-solve-the-equation-2-2x2/582144/40 "2011-05-18T21:53:58Z")
at least in algebra 2 as currently being taught in NC, you can, pulykamell. I’ve been helping my son with homework in that and “root” is used as a synonym for “zero” and his questions on homework ask “what are the roots” or “what are the zeroes” of various rational expressions and polynomials like your examples
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