5s^2 - 10s = 23

First we factor out the leading coefficient
on the left

5(s^2-2s) = 23

We complete the square inside the parentheses by 

1. Taking 1/2 of -2, the coefficient of s, getting -1
2. Squaring the result of step 1, (-1)^2 = +1.
3. Adding that inside the parentheses.

5(s^2-2s+1) = 23+5

Adding +1 inside the parentheses on the left side amounts to 
adding +5 to the left side because of the 5 before the 
parentheses that we factored out.

So we add +5 to both sides of the equation by adding +1
inside the parentheses on the left, and +5 to the right side.

Edwin