Question

In the function f(x) = (x^2 -6x + ___) + 20, what number belongs in the blank to complete the square?

Answer 1

blank = -11

Explanation:

The given function is :

`f(x) = (x^2 -6x+x)+20`

We need to find the number x such that it forms the complete square.

If x = -11, then it will becomes,

`f(x) = (x^2 -6x+(-11))+20\\\\f(x)=x^2-6x+9`

We can write it as follows :

`f(x)=x^2-2(1)(3x)+(3)^2` ..(1)

We know that,

`(a-b)^2=a^2-2ab+b^2` ...(2)

Comparing (1) and (2).

`f(x)=(x-3)^2`

So, if we put the blank equals -11, then it will become the perfect square.