Find the sum of all values of $k$ for which $x^2 + kx - 9x + 25 - 9$ is the square of a binomial.
+36916 x^2 + kx - 9x + 25 - 9 =
x2 + x(k-9) + 16 the only two binomial squares that this matches are ( x-4)2 and (x+4)2
expanding these : x^2 - 8x + 16 and x^2 + 8x + 16
then k - 9 = -8 k-9 = 8
shows k = 1 shows k = 17
Sum the two possible values of k : 1 + 17 = 18
+36916 x^2 + kx - 9x + 25 - 9 =
x2 + x(k-9) + 16 the only two binomial squares that this matches are ( x-4)2 and (x+4)2
expanding these : x^2 - 8x + 16 and x^2 + 8x + 16
then k - 9 = -8 k-9 = 8
shows k = 1 shows k = 17
Sum the two possible values of k : 1 + 17 = 18
