Question

What must be added to x²+x to make it a perfect square

Answer 1

For a more general perfect square rule, you get the coefficient of the x term (in this case, it’s 2.)

Divide that by 2, because you have to have the same constant-term within your brackets.

You can then use bracket expansion to get the last term.

i.e.

x^2 + Bx + ? -> (x + B/2) (x + B/2)

so the last term is (B/2)^2.

In this case, B is 2, so the last term is 1.