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:
\(\frac{6+-\sqrt{128}}{2}\), or \(3+-4\sqrt{2}\). The line intersects the parabola at two points, \(3+4\sqrt{2}\) and \(3-4\sqrt{2}\).
