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Use an operational amplifier to make a virtual ground, then between ground and virtual ground you have a negative voltage that you can use to your negative voltage divider ... but all your circuit have to be referenced on virtual ground.
You can generate negative voltage from positive.
Try to employ 555 timer as negative voltage generator (see picture below).
To regulate negative voltage you can place at the output a zener diode of required value ..
Regards,
IanP
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