SOLUTION: The square root of 3n + 6 = 4 - n I'm sorry but I do not even know where to start

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Question 807612: The square root of 3n + 6 = 4 - n
I'm sorry but I do not even know where to start

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Probably you meant sqrt%283n%2B4%29=4-n
(That can be written as sqrt(3n+4)=4-n>

To solve equations that have a square root on one side of the equal sign,
your fist step would be squaring both sides of the equal sign.
You may be adding some "extraneous solutions" by doing that,
but you can eliminate extraneous solutions at the end.

%28sqrt%283n%2B6%29%29%5E2=%284-n%29%5E2 has all the solutions of sqrt%283n%2B4%29=4-n ,
and maybe a few more solutions.
%28sqrt%283n%2B6%29%29%5E2=%284-n%29%5E2
3n%2B6=16-8n%2Bn%5E2
0=n%5E2-8n%2B16-3n-6
n%5E2-11n%2B10=0
The quadratic equation
n%5E2-11n%2B10=0 can be factored to find the solutions.
The factored equation
%28n-1%29%28n-10%29=0 indicates that the solutions derive from
n-1=0 --> highlight%28n=1%29
and n-10=0%29%7D%7D+%3C--%3E+%7B%7B%7Bn=10 , which would make
sqrt%283n%2B6%29%29=4-n=-6 , which does not make sense.
So the only solution the original equation is highlight%28n=1%29 .