$$ x^2 - x - 2 = 0 $$
$$ (x-2)(x+1) = 0 $$
$$ x = -1, 2 $$
in the given example, (x-2)(x+1) where x is -2 and +1 why did the last line of the example was swap?
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J. M. ain't a mathematician
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ilovetolearn
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2Don't read too much into it; it's the same as saying $x=2$ and $x=-1$. Note that if you solve $x+1=0$ for $x$, you get $x=-1$. – J. M. ain't a mathematician May 03 '11 at 13:34
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2$x - 2 = 0$ doesn't imply that $x = -2$. – Qiaochu Yuan May 03 '11 at 13:34
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$(x-2)(x+1)=0$ $\Leftrightarrow$ $x-2=0 \lor x+1=0$ $\Leftrightarrow$ $x=2 \lor x=-1$. Is this what you're asking? (You're question does not sound very clear to me.) – Martin Sleziak May 03 '11 at 13:35
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so in this case I can also choose $$ x = 1, -2 $$ – ilovetolearn May 03 '11 at 14:18
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1@liangteh, No. please make sure you understand what Martin said. – Jiangwei Xue May 03 '11 at 14:43
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@liangteh, remember that you can always check your answer by plugging them into your original equation. What happens if you plug in 1 or -2? What happens if you plug in -1 or 2? The last result is reached by solving $x-2=0$ and $x+1=0$. What are the solutions to these equations? – Calle May 03 '11 at 15:04
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In the real numbers (and complex numbers, and integers, and rationals), if a product is equal to $0$, then at least one factor is equal to zero.
So for $(x-2)(x+1)$ to be equal to zero, either $x-2=0$, or $x+1=0$.
However, for $x-2$ to equal $0$ you don't need $x$ to be equal to $-2$, you need it to be equal to $2$: $x-2=0$ is equivalent to $x=2$. And for $x+1=0$ to be true, you need $x=-1$. So that's why you go from "$x$ minus $2$" to $x=2$, and from "$x$ plus $1$" to $x=-1$.
(In general, $x$ equals $a$ if and only if $x-a=0$. And $x+1 = x-(-1)$).
t.b.
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Arturo Magidin
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Somehow I am reminded of the rant somewhere in this site (was it you?) about the use of the word "negative"... – J. M. ain't a mathematician May 03 '11 at 16:29
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@J.M. I wouldn't call it a "rant", but perhaps you are thinking of the last sentence in the penultimate paragraph of http://math.stackexchange.com/questions/13094/significance-of-displaystyle-sqrtnan/13095#13095 – Arturo Magidin May 03 '11 at 16:31
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