If 554_b is the base b representation of the product of 34_b and 15_b, then find b.
+2666 Simplify to: \(5b^2 + 5b + 4 = (3b + 4)(b + 5)\)
Simplify the right-hand side to: \(5b^2 + 5b + 4 = 3b^2 + 19+ 20\)
Move everything to the left-hand side to make a quadratic: \(2b^2 - 14b - 16 = 0\)
Factor as: \(2(b+1)(b-8) = 0\)
The only solutions are -1 and 8, but b must be positive, meaning \(b = \color{brown}\boxed{8} \)
