Explanation:
x² - 12x + 32 = 0
the goal is the vertex form : a form like
(x - h)² + k = r²
with (h, k) being the vertex or center and r the radius.
doing all the multiplications we get
x² - 2hx + h² + k - r² = 0
and we compare this with our original equation. we see
x² = x²
-12x = -2hx
-12 = -2h
6 = h
32 = h² + k - r²
32 = 36 + k - r²
-4 = k - r²
possible solution : k = 0 and then r = 2
but also e.h. k = 12, r = 4
so, without the information about e.h. the radius we cannot identify one solution.
so, "A" vertex form (one of many possible ones) is
(x - 6)² = 4