[Araconan]

I am currently attempting the following problem:

Nitric oxide and bromine react accordingly to the following reaction:

2NO(g) + Br₂(g) <----------> 2NOBr(g)

The equilibrium constant at 300K is 134 atm^-1

What would be the partial pressures of all species if NO and Br₂, both at an initial partial pressure of 0.3 atm, were allowed to come to equilibrium at this temperature?

My attempt:

Because the equilibrium constant is relatively large, I'm going to assume that the forward reaction goes towards completion

Creating an ICE table:
                           2NO(g) + Br₂(g) <----------> 2NOBr(g)
Initial:                 0.3           0.3                       0
Change:             -0.3          -0.15                    +0.3
Equilibrium:         0              0.15                     0.3

Considering the reverse reaction:
If I reverse the reaction, the equilibrium constant of the reverse reaction would be equal to 134^-1

Creating an ICE table:
                           2NOBr(g) <----------> 2NO(g) + Br₂(g)
Initial:                 0.3                             0             0.15
Change:             -2x                              +2x         +x
Equilibrium          0.3 - 2x                       2x          0.15 + x

The equation would be:

(2x)²(0.15+x)/(0.3-2x)² = 134^-1

Because the equilibrium constant is very small, I'm going to assume that x is negligible, and thus the equation becomes:

(2x)²(0.15)/(0.3)²

Solving for x gives me 0.033, while the textbook, using successive approximations (it didn't consider the reverse reaction, and just solved the equation from the original reaction) got 0.026.

I'm wondering, did I do something wrong? Or is my answer more accurate than the textbooks? 

Thank you in advance!