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check for extraneous solutions. sqrt x+7-x=1 Please show step by step on how to do this. Thankyou.

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Let \(u=\sqrt{x}\), then x = \(u^2\) Now, the equation becomes \[u+7-u^2=1\] Can you do it?

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Other answers:

I don't get the way you're explaining it to me @RolyPoly
Please make use of parentheses. The way you write problems is sorta confusing. Is it √(x+7)-x=1 or ...?
I guess. Sorry, it doesn't show parentheses on my math problem.
Is the equation (1)\(\sqrt{ x+7-x} =1\) or (2) \(\sqrt{x}+7-x=1\)?
nvm, i got the answer. Thx
nvm.. I tried wolframalpha. But only get two step by steps each day:(
I'll have to get the answer tomorrow.
It would be better if you know how to solve it, instead of just relying on WolframAlpha.
eh, true. But lets be honest with ourselves, I'm never going to use this advanced of math in the future.
Honestly, I just need credits/passed classes
you can argue all you want, but it's true.
Don't want to argue, just want to help you pass the course and you can learn how to solve it at the same time :)
can you just show me please? I'm 18 lessons behind:(
add x to both sides
It would be a different story if I wasn't that behind
\[\sqrt{x-7-x}=1\]\[\sqrt{x-7}-x=1\]\[\sqrt{x}-7-x=1\] Which one is your question?
like this @nikato |dw:1388896983931:dw|
the 2nd one @RolyPoly
what next?
so now u have|dw:1388897108757:dw| now square both sides
i know 9 is the solution
what next?
did u square both sides. and simplified it?
how do I simplify it?
|dw:1388897450469:dw|does that make sense?
what next?
subtract x and 7 on both sides so that the equation equal 0
what next? :D ha
|dw:1388897800670:dw| can u factor the right side?
can you show me? eheh
it has to be 9.
no, i dont think 9 is a solution. try pluggin it back into the origianl equation. it doesnt work
then you did it wrong. Ugh. Wolfram said it was 9
no, im for sure 9 is not an answer. it doesnt make sense. its one fo those^
@Krazete is he wrong or not?
sorry, nikato. I gotta make sure.
yea, its fine. whatever u feel is right
nikato's right.
okayy,, it's just wolfram said the solution was 9. But I guess it's better to have something than nothing at all.
maybe u typed in the wrong equation in wolfrma
Look at what Wolfram says under "input." Is it the same as your problem? It might've calculated √x instead of √(x+7). Parentheses are quite important.
nikato, what do I do next? Sorry for doubting you
|dw:1388899779946:dw| solve for x. did most of the work. should be easy for u. there are suppose to be 2 answers
one of them is 2.
yes. and the other?
no, -3. so now u want to find if there is anyextraneous answers
plug both back into the equation and see if they make sense|dw:1388900195738:dw|
ugh. How much more is there??
what next?
no, this is it. check if both of those equation are true. if they are not, then that "x" is extraneous
it's 1.
thanks. :p
WAIT NO. its either 2 or -3. i helped plug in both in for x the first one is x=2 and the other is x=-3
I did it in my calculator. How'd you get your answer?
no, thats not what i meant
I'm sorry, I still don't get how you got those answers. I got -5 and 1. 1 was correct. -5 was incorrect.
yes. so that means -3 is the extraneous answer. remember how we worked the problem, and got 2 and -3 as the naswer. however when u plug -3 back into the original equation u get -5 instead of 1. which means the answer doesnt "work" which we call an extraneous answer
so what is the answer???
just 2
becuz like i said ^ -3 is an extraneous solution
so, I would put "x=2 only"?

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