Question

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

Answer 1

Answer:

blank = -11

Step-by-step 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.