This representation is fine for your purposes - no need to use the completed square form.
To arrive at this solution, you should set the expression (x^2-6x+18) equal to 41, and solve the resulting quadratic. Subtract 41 from both sides to get x^2-6x-23, and from there, apply the quadratic formula to get:
[tex] \frac{6+-\sqrt{128}}{2} [/tex], or [tex]3+-4\sqrt{2} [/tex]. The line intersects the parabola at two points, [tex]3+4\sqrt{2}[/tex] and [tex]3-4\sqrt{2}[/tex].
