#### Answer

True.

#### Work Step by Step

Factor the trinomial by looking for the factors of $-63$ whose sum is equal to the middle term's coefficient of $2$.
These factors are -7 and 9. This means that the factored form of the trinomial is $(x-7)(x+9)$
Thus,
$x^2+2x-73=0
\\(x-7)(x+9)=0$
Equate each factor to 0, and then solve each equation to obtain:
$x-7=0 \text{ or } x+9-0
\\x=7 \text{ or } x=-9$
The solution set is $\left\{-9, 7\right\}$.
Therefore, the given statement is true.