Posted by **miss b** on Wednesday, December 19, 2012 at 8:47pm.

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

- math... Ms, Sue can you help? -
**Reiny**, Wednesday, December 19, 2012 at 10:31pm
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)(2b-3)

= 2b^2 + b - 6 , the original.

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