The distance between the points $A$ and $B$ is $\sqrt{34}.$ If $A = (a,4)$ and $B = (-20,33),$ then find the sum of all possible values of $a.$
(a - -20)^2 + (33 - 4)^2 = 34
(a + 20)^2 + 29^2 = 34
(a + 20)^2 = 34 - 29^2
(a + 20)^2 = -807
No such real values for a since the left side can only be positive or 0
+1459 
