Question

What value is needed to complete the square? All steps included

Answer 1

The correct answer is 9.

Explanation:

Using the Special Factoring Formula for Perfect square:

`u^(2) - 2uv + v^(2) = (u - v)^(2)`

Since we have the given,
`x^(2) - 6x + __` ___,

We must think of a factor that adds up to -6x, and must lead to a perfect square.

A way to do this is by taking the coefficient middle term, -6, dividing it by 2, and squaring it:

`((6)/(2))^(2) = (3)^(2) = 9`

Therefore, the missing constant term is 9.

To check whether it is correct, we can take
`(x - 3)^(2)`, and multiply using the FOIL method. We'll have the following answer:

`(x - 3) (x - 3)`

`= x^(2) - 3x - 3x + 9`

`= x^(2) - 6x + 9`

Therefore, we came up with the correct constant that completes the square, which is 9.