Subtracting fractions

Question

I was watching this video: https://www.youtube.com/watch?v=aSId_Kgjzfg&index=55&list=PLg2tfDG3Ww4vrstKAZ0dajHx_hq85P0G

At 10:25 I saw the following fractions subtracted on the third line going upwards:

-1/8 -152/8 = 153/8

Why is the answer not in negative form?

Answer 1

If you have $X - a =0$ then you add $a$ to both sides of the equation to get.

$X -a + a = 0 + a$

$X = a$

So in the video he has

$2(x+ \frac 14)^2 - \frac 18 - \frac {152}8 = 0$.

then he did the following steps in his head without writing them on the board.

...$2(x+ \frac 14)^2 - \frac {153}8 = 0$....

...$2(x+ \frac 14)^2 - \frac {153}8+ \frac {153}8= 0+ \frac {153}8$...

And concluded

$2(x+\frac 14)^2 = \frac {153}8$.

Answer 2

Because $2(x + \frac{1}{4})^2 - \frac{1}{8} - \frac{152}{8}= 0$ if and only if $2(x + \frac{1}{4})^2 = \frac{1}{8} + \frac{152}{8}=\frac{153}{8}$. Note that the right hand side changes at this step which is why the term is now positive.