Answer
The solution set is $\left\{1, 8\right\}$.
Work Step by Step
Factor the trinomial by looking for the factors of 8 whose sum is equal to the coefficient of the middle term (-9).
These factors are $-8$ and $-1$. This means that the factored form of the trinomial is $(x-8)(x-1)$.
Thus,
$x^2-9x+8=0
\\(x-8)(x-1)=0$
Equate each factor to 0 then solve each equation to obtain:
$x-8=0 \text{ or } x-1=0
\\x=8 \text{ or } x=1$
The solution set is $\left\{1, 8\right\}$.
