Question

find the real solutions of the equation.$(x+2)^2 + 11(x+2) + 18 = 0$what is the solution set? select the correct choice below and fill in any answer boxes in your choice.a. the solution set is {}.(use a comma to separate answers as needed. rationalize all denominators. type an integerb. there are no real solutions.

Explanation:

Step1: Substitute $u=x+2$

$u^2 + 11u + 18 = 0$

Step2: Factor the quadratic

$(u+2)(u+9) = 0$

Step3: Solve for $u$

$u+2=0 \implies u=-2$; $u+9=0 \implies u=-9$

Step4: Substitute back $u=x+2$

For $u=-2$: $x+2=-2 \implies x=-4$
For $u=-9$: $x+2=-9 \implies x=-11$

Answer:

A. The solution set is $\{-11, -4\}$