If 554_b is the base b representation of the product of 34_b and 15_b, then find b.
+128474 34 can be written as 3b + 4
15 can be written as 1b + 5
554 can be written as 5b^2 + 5b + 4
So we have that
(3b + 4) ( 1b + 5) = 5b^2 + 5b + 4
3b^2 + 19b + 20 = 5b^2 + 5b + 4 simpify as
2b^2 - 14b - 16 = 0
b^2 - 7b - 8 = 0 factor
(b - 8) ( b + 1) = 0
Only b - 8 provides a solution
b - 8 = 0
b = 8
