math... Ms, Sue can you help?
posted by miss b on .
Apparently, I got this question wrong on a test and I'd like to know what error I made... can you help?
Here's what I did:
2b^2+b=6
b^2+1/2b=3
b^2+1/2b+(1/2)^2=3+(1/2)^2
(b+1/2)^2=3+1/4
b+1/2=+/ <13/4>
b=1/2+/<13>/2
b=(1+/<13>)/2
<> means its in a radical and +/ means plus or minus

The error is in your third line
you take 1/2 of the middle coefficient, and then square it
(1/2)(1/2) = 1/4  (1/4)^2 = 1/16
3rd line:
b^2 + (1/2)b + 1/16 = 3 + 1/16
(b+1/4)^2 = 49/16
b + 1/4 = ± 7/4
b = 1/4 ± 7/4 = 6/4 or 8/4
b = 2 or 3/2
since we have rational answers, we know it would have factored to
(x+2)(2b3)
= 2b^2 + b  6 , the original.