Question

Given that 221 base x =25 base 10..find the base of x

Answer 1

If $221_x=25_{10}$, then

$2x^2 + 2x + 1 = 25$

Solve for x :

$2x^2+2x-24=0 \\\\ x^2 + x - 12 = 0 \\\\ (x+4)(x-3) = 0 \\\\ \boxed{x = -4 \text{ or }x=3}$

(Yes, bases can be negative.)