Answer:
blank = -11
Step-by-step explanation:
The given function is :
[tex]f(x) = (x^2 -6x+x)+20[/tex]
We need to find the number x such that it forms the complete square.
If x = -11, then it will becomes,
[tex]f(x) = (x^2 -6x+(-11))+20\\\\f(x)=x^2-6x+9[/tex]
We can write it as follows :
[tex]f(x)=x^2-2(1)(3x)+(3)^2[/tex] ..(1)
We know that,
[tex](a-b)^2=a^2-2ab+b^2[/tex] ...(2)
Comparing (1) and (2).
[tex]f(x)=(x-3)^2[/tex]
So, if we put the blank equals -11, then it will become the perfect square.
