Question

(X+4)^2=-18 solve by extracting roots

Answer 1

Solve for x:
(X + 4)^2 = -18 x

(X + 4)^2 = -18 x is equivalent to -18 x = (X + 4)^2:
-18 x = (X + 4)^2
Divide both sides by -18:
Answer:  x = -1/18 (X + 4)^2

Answer 2

We are to solve (X+4)^2=-18 for x.

Start by taking the sqrt of both sides:  x+4 = plus or minus sqrt(-18) = plus or minus  sqrt(-1)*sqrt(9)*sqrt(2)

Then x + 4 = plus or minus (i)(3)sqrt(2)

We must solve for x.  Subtr. 4 from both sides, obtaining:

x = -4 plus or minus (i)(3)sqrt(2)     These are the roots you wanted.
We say these roots are "complex" because of the imaginary components.