That still wouldn't equal the answer given in the textbook. The answer is: (2 +- sqrt2)/2

Okay, you found:

$x=1\pm\sqrt{\frac{1}{2}}$

Now, let's multiply this by $1=\frac{2}{2}$

$x=\left(1\pm\sqrt{\frac{1}{2}} \right)\cdot\frac{2}{2}= \frac{2\left(1\pm\sqrt{\frac{1}{2}} \right)}{2}= \frac{2\pm\sqrt{2}}{2}$

Okay, thanks.

This is going to sound really stupid, but it's just to clarify my understanding: How does 2 x sqrt(1/2) = sqrt2?

$2\sqrt{\frac{1}{2}}=2\cdot\frac{1}{\sqrt{2}}=\frac {(\sqrt{2})^2}{\sqrt{2}}=\sqrt{2}$