Question

find the real solutions of the equation.
$(x+2)^2 + 11(x+2) + 18 = 0$

Explanation:

Step1: Substitute $u = x+2$

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

Step2: Factor the quadratic equation

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

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:

$x=-11$ and $x=-4$