We will solve as follows:
![w^2-12w+\alpha=0](https://img.qammunity.org/2023/formulas/mathematics/college/8zumopvp3q8yyg5rng6o6d06nw9scllpme.png)
Here alpha is the blank space, we then will solve by factoring:
![(w+b)(w+c)=w^2-12w+\alpha](https://img.qammunity.org/2023/formulas/mathematics/college/avun6uir6s6hfkmrwzby62s50iixfpw8i6.png)
*Two numbers that added equal -12 can be -10 and -2 and when multiplied they equal to 20, then we will have that alpha will be equal to:
![w^2-12w+20=0](https://img.qammunity.org/2023/formulas/mathematics/college/xt26q6cu6wi76lnsj4stg2uz95ym8j7k7m.png)
Then, the final expression is:
![w^2-12w=-20](https://img.qammunity.org/2023/formulas/mathematics/college/qrebzbtelbplcaqjwobb3cszuxtz2wnp3b.png)