Question

In the function f(x) = 5(x2 − 4x + ____) + 15, what number belongs in the blank to complete the square?

Answer 1

Take the 'b' value and divide by 2, then square that number, add it in the blank.
-4/2 = -2
(-2)^2 = 4
4 goes in the blank

Answer 2

The number in the blank is 4.

Explanation:

Notice that we want to complete the square in the expression
`x^2-4x+____`.

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
`(x-a)^2`.

We deduce that the sign is a minus because the sign of the middle term is also a minus.

Expanding:

`(x-a)^2 = x^2 -2ax +a^2`. Then, we equate
`2a=4` and we deduce that
`a=2`. Thus, the number in the blank is
`a^2 = 2^2=4`.