(35s 42s/DM42 50G) Quadratic formula

[mchris]

Probably someone has done it before, but...
Inspired by a HP41C program I found for the quadratic formula that uses only the 4 level stack, no INPUTs, no extra registers, I thought maybe I could do something similar with the HP35s, despite that it doesn't have the register arithmetic with the stack registers. The program uses the equivalent formula -(b/2a)±SQRT((b/2a)^2-(c/a)). The fact there is only 2 terms makes it easier. I don't think it could be done with the (-b±SQRT(b^2-4ac))/2a formula. We press a ENTER b ENTER c XEQ Q and the 2 solutions, real or complex returned in X and Y registers. No INPUTs, no extra registers, just the stack, in just 29 steps.

Code:

Q001        LBL Q
Q002        EQN REGZ
Q003        /
Q004        RDN
Q005        X<>Y
Q006        /
Q007        2
Q008        /
Q009        +/-
Q010        ENTER
Q011        X^2
Q012        RUP
Q013        -
Q014        X>=0?
Q015        GTO Q021
Q016        +/-
Q017        SQRT
Q018        i
Q019        *
Q020        GTO Q022
Q021        SQRT
Q022        ENTER
Q023        ENTER
Q024        EQN REGT
Q025        +
Q026        RDN
Q027        -
Q028        RUP
Q029        RTN