SOLUTION: Pls do help :{{{if 25 * 14 =374 find the number base used}}}

Question 936933: Pls do help :
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
let x be our number base, then
25 = 2x+5
14 = x+4
374 = 3(x^2)+7x+4, therefore
(2x+5)*(x+4) = 3(x^2)+7x+4
2x^2 + 13x + 20 = 3x^2 +7x + 4
x^2 -6x -16 = 0
factor polynomial
(x-8)*(x+2) = 0
x = 8 or -2
either base will work, however, we mostly use positive bases.
in your problem
25 base 8 is 21
25 base -2 is 2*(-2) + 5 = 1
14 base 8 is 12
14 base -2 is 2
374 base 8 = 3*64 + 56 + 4 = 252
374 base -2 = 3*(4) + 7(-2) +4 = 2
1) for base 8 we have
21*12 = 252
252 = 252
2) for base -2 we have
2 *1 = 2
2 = 2
our answers check

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