Question 188987: radical b^2+16+2b = 5b
b^2 + 16 + 2b = 25b^2
0 = 24b^2 - 2b - 16
0= 2(12b^2 - b - 8)
then what?
I know the answer is the square root of 2, but don't know how to get there from here.
Thanks
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
So, you know the answer is  . Well, let's just find out if that is correct.
If
and
then
^2 + 16 + 2( \sqrt{2})} = 5 sqrt{2})
Well, root 2 squared is just 2 plus 16 is 18 plus 2 times root 2 which is a little less than 3, so total somewhere between 20 and 21, take the root of that and you get maybe 4 and a half. But 5 times root 2 is a little less than 7 and a half. < Buzz > Thank you for playing, we have some lovely parting gifts.
Once you have
)
You know that
Just use the quadratic formula:
Where  ,  , and 
^2 - 4(12)(-8)}}{2(12)})
You get to do your own arithmetic.
You will get two roots to the quadratic, but in the process of squaring the variable you quite often get an extraneous root. One of the roots to this equation will be extraneous, so you have to check both answers in the original equation to determine which one to throw out.
John
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