Answer
$\left\{-10, -1\right\}$
Work Step by Step
Move all terms to the left side. Note that when a term moves to the other side of the equation, the sign changes to its opposite.
$x^2+11x+10=0$
With a leading coefficient of $1$, factor the trinomial by looking for factors of the constant term $(10)$ whose sum is equal to the coefficient of the middle term $(11)$.
Note that $10=(10)(1)$ and $10+1 = 11$.
This means that the factors of the trinomial are $x+10$ and $x+1$.
Thus, the factored form of the trinomial is:
$(x+10)(x+1)=0$
Equate each factor to zero then solve each equation to obtain:
$x+10 = 0 \text{ or } x+1=0
\\x=-10 \text{ or } x=-1$
The solution set of the given equation is $\left\{-10, -1\right\}$.
