What number should be added to the expression to turn it into a perfect square trinomial x^2+2x

Kinda like completing the square
if you have
ax^2+bx+c
a=1 for ease

take b and halve it then square that
then make c= that

x^2+2x+c
a=1 good
b=2
2/2=1
1^2=1
x^2+2x+1
(x+1)^2

the number 1 should be added

Solutions 

A Perfect Square Trinomial is the product of two binomials. Both the binomials are same. When you multiply an algebraic expression with two terms to itself, you will get a three-term expression called a perfect square trinomial. A perfect square trinomial is one that factors into two identical factors. The general forms of perfect square trinomial are = 

(ax - b)² = (ax)² - 2axb + b² and (ax + b)²= (ax)² + 2axb + b²

Calculations 

αx²+βx+c

The variable α = 1 for ease

Take the variable b and half it then square that
to make c = number

x²+2x+c

variable α = 1 

variable β = 2 

2 ÷ 2=1

1² = 1 

x²+2x+1

(x+1)² 

In conclusion the number (1) should be added to the expression to turn it into a perfect square trinomial . 

24 + 4 = 28
14 • 2 = 28
11 • 2.57 = about 28

Hope this helps a little!