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

Sagot :

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.

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