That still wouldn't equal the answer given in the textbook. The answer is: (2 +- sqrt2)/2
Okay, you found:
$\displaystyle x=1\pm\sqrt{\frac{1}{2}}$
Now, let's multiply this by $\displaystyle 1=\frac{2}{2}$
$\displaystyle x=\left(1\pm\sqrt{\frac{1}{2}} \right)\cdot\frac{2}{2}= \frac{2\left(1\pm\sqrt{\frac{1}{2}} \right)}{2}= \frac{2\pm\sqrt{2}}{2}$
Your answer is equivalent to that given by your textbook, just in a different form.