Question 58901
Yes you are right.
23x^2 + 17x + 11 = 0 cannot be factored.
Even if you try to use the formula , the solution is not real.

The second one is 1 + Sqrt(x-5) = 0
                ==> sqrt (x-5) = -1 [ adding -1 to both the sides]
                ==>  x - 5 = 1 [Squaring both the sides]
                ==>  x = 6 [Adding 5 to both the sides]

So x = 6 and the given eqn is satisfied only for negative sqrt.

Regards,
Uma