X^2 + 2x = 1
To make it a perfect square, you must add 1 to both sides.
x^2 + 2x + 1 = 1 + 1
x^2 + 2x + 1 = 2
Then we factor it to prove if its factors when multiplied will be equal to x^2 + 2x +1...
(x + 1)(x + 1) = 2
Since, it has two common factors then it is a perfect square.