Question

How do you complete the square for `x^2+7x`?

Answer 1

Note that `(x+7/2)^2 = x^2+7x+49/4`

So `x^2 + 7x = (x+7/2)^2 - 49/4`

Explanation:

In general:

`ax^2+bx+c = a(x+b/(2a))^2 + (c - b^2/(4a))`

In the common cases where `a=1` this simplifies to:

`x^2+bx+c = (x+b/2)^2 + (c - b^2/4)`