# Rational Completeing the Square

1. Feb 3, 2013

### ISX

1. The problem statement, all variables and given/known data

2. Relevant equations

3. 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.

2. Feb 3, 2013

### SammyS

Staff Emeritus

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

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 .

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3. Feb 3, 2013

### Dansuer

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

and not to

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

4. Feb 3, 2013

### ISX

Hellllllll I've been doing it wrong for centuries then. Lets 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.