Question

What number should be added to make this a perfect square trinomial?
This is called ʺcompleting the squareʺ of the expression. x^2-1/3x?

Answer 1

x^2-(1/3x)

Answer 2

You want to write it as (x + a)^2 = x^2 - (1/3)x + b, where b is this number you have to add.

( (x+a)^2 is the perfect square thing. )

Expanding, (x+a)^2 = x^2 + 2ax + a^2. And you want that to be equal to x^2 + (1/3) x + b.

So you know that 2a = 1/3, so a = 6. So you know that b = a^2 as well. So b = 36. So to make it a perfect square you have to add 36. I think that's right. I haven't solve quadratics in ages.