Which of the following are solutions to the equation below?

Check all that apply.

x^2 + 4x + 4 = 12

A. x = - √2+12

B. x = √2+12

C. x = - 2√3-2

D. x = - 2√3+2

E. x = 2√3-2

F. x = 2√3+2

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.