Rational Completeing the Square

[ISX]

Homework Statement

Homework Equations

The Attempt at a Solution

Alright so the solution is in the above pic, but I can't get anywhere close. You can see from the green circles that the "squares" aren't matching up. So I'm not sure if I can't multiply fractions anymore or what.

 

[SammyS]

Homework Statement

[ IMG]http://i49.tinypic.com/51v52u.jpg[/PLAIN]

Homework Equations

[ IMG]http://i50.tinypic.com/9fxswl.jpg[/PLAIN]

The Attempt at a Solution

Alright so the solution is in the above pic, but I can't get anywhere close. You can see from the green circles that the "squares" aren't matching up. So I'm not sure if I can't multiply fractions anymore or what.
[ IMG]http://i47.tinypic.com/2ivzmoj.jpg[/PLAIN]

Your line

\displaystyle x^2-\frac{5}{6}x+\frac{25}{144}=-\frac{1}{6}+\frac{25}{144}

is correct.

What your last line shows (correctly) is that \displaystyle \left(x-\frac{5}{6}\right)^2\ne x^2-\frac{5}{6}x+\frac{25}{144}\ .

When you square 5/6, you don't get 25/144 .

How did you get 25/144 in the first place? You squared 5/12 not 5/6 .

 

[Dansuer]

you went from
x^2 +bx + (\frac{b}{2})^{2}
to
(x+b)^{2}

and not to

(x+\frac{b}{2})^{2}

 

[ISX]

Hellllllll I've been doing it wrong for centuries then. Let's try this again.

Ahhhh! Thanks for the help guys! I was always just dropping the last number off and went with the first 2. Guess I never caught on that fractions didnt work that way.