Answer:
The number in the blank is 4.
Step-by-step explanation:
Notice that we want to complete the square in the expression [tex]x^2-4x+____[/tex].
A way to do this is use a method call as undetermined coefficients, which looks complicated but it is not. Well, we want to convert the above expression in something like [tex](x-a)^2[/tex].
We deduce that the sign is a minus because the sign of the middle term is also a minus.
Expanding:
[tex](x-a)^2 = x^2 -2ax +a^2[/tex]. Then, we equate [tex]2a=4[/tex] and we deduce that [tex]a=2[/tex]. Thus, the number in the blank is [tex]a^2 = 2^2=4[/tex].
