For how many integer values of k between -6 and 6, inclusive, does the equation x² + kx + 9 = 0 have exactly one real solution?

A quadratic has exactly one real solution when its discriminant is zero. For $x^2 + kx + 9 = 0$, the discriminant is $k^2 - 36$, so $k^2 = 36$ and $k = 6$ or $k = -6$. Both are integers in the range from $-6$ to $6$ inclusive. Check: $x^2 + 6x + 9 = (x+3)^2$ and $x^2 - 6x + 9 = (x-3)^2$, each with a single root. So there are 2 values. A common wrong answer is 1, from counting only the positive value, and another is 13, from counting every integer in the range. Remember that squaring gives two roots, positive and negative.