I was getting a little tired of being a layman so I decided that I would try doing some math. Then I think I have found a flaw with factor by grouping. Maybe I was just doing it wrong, but I double checked it. Then it seems to come wrong every time I try to work a problem in this type of fashion (using factor by grouping). For example, solve for x: \(9{(2x-1)}^{2}+2=-9(2x-1)\) \(2=-9(2x-1)-9{(2x-1)}^{2}\) Brought 9(2x-1) to the right side. \(2=-9(2x-1)(1+(2x-1))\) Factored out a -9(2x-1) out of the right side. \(2=-9(2x-1)(2x)\) The ones cancel each other out. \(2=-18x(2x-1)\) Multiplied the 2x by -9. \(2=-36x+18x\) Distributed the -18x. \( 2=-18x\) Added like terms \(-\frac{2}{18}=x\) Divided both sides by -18. \(x=-\frac{1}{9}\) Moved to the other side and simplified. These where supposed to all be valid operations in algebra. Then checking the answer, if you put -1/9 into the original equation, both sides didn't equal each other. Then if I just multiply everything out and then add like terms, I got a different answer (that is supposed to be the correct answer) {x|x 1/3, 1/6}.
Never mind, I see what I did now. Forgot to square the x on -36x for some reason. Must be getting old or something.
