There are several ways in which we could answer this question. My choice is to actually solve the given quadratic equation, x^2 + 4x + 4 = 12.
Note that x^2 + 4x + 4 is a perfect square. Thus,
x^2 + 4x + 4 = 12 is the same as (x+2)^2 = 12, so that
x+2 = plus or minus √3*√4, or plus or minus 2√3.
Thus, the two real, unequal roots are
x = -2 + 2√3 and x = -2 - 2√3. These correspond to answer choices C and E.
