Let f(x) = x^2 + bx + 12 - 3x + 10 for all real numbers $x$. Find the greatest integer value of $b$ such that $-4$ is not in the range of $f(x)$.
x^2 + (b-3)x + 22 > -4
x^2 + (b-3)x + 26 > 0
Set the discriminant to < 0
(b - 3)^2 - 4(1)(26) < 0
(b -3)^2 < 104
b -3 < [ sqrt 104]
b- 3 < ≈ 10.2
b < ≈13.2
Greatest integer value of b = 13
+789 
