Solve x²+10x+9=0: Finding the Number of Solutions

Let's observe that the given equation:

$x^2+10x+9=0$is a quadratic equation that can be solved using quick factoring:

$x^2+10x+9=0 \longleftrightarrow\begin{cases}\underline{?}\cdot\underline{?}=9\\ \underline{?}+\underline{?}=10\end{cases}\\ \downarrow\\ (x+1)(x+9)=0$and therefore we get two simpler equations from which we can extract the solution:

$(x+1)(x+9)=0\\ \downarrow\\ x+1=0\rightarrow\boxed{x=-1}\\ x+9=0\rightarrow\boxed{x=-9}\\ \boxed{x=-1,-9}$and therefore the given equation has two solutions,

Thus, the correct answer is answer B.