Question

What do you need to add to complete the square for `x^2+8x`?

Answer 1

16

Explanation:

Since the `8x` is positive, the equation `(x+y)^2` must have `y` as a positive number. Let's see this!

An easy way to complete the square if you have the constants for `x^2` and `x` but not the non-variable number is to divide the `x` constant, and then square it. Just like this:

`8x`/`2` `=4`.
`4^2=16`.

The last number must be 16. Let's check it.

`(x+4)^2=x^2+8x+color(red)16`

The answer is `16`.

Yay!