how do you solve equations by completing the square

This James Tanton video should help: https://www.youtube.com/watch?v=OZNHYZXbLY8 

Here's an example:

x^2+3x-5=0                  First move your imperfect "c" (-5) to the other side. Leave room for new c

x^2+3x    =5                 To make new c, take a half of "b" (3)and square it. Add to both sides.

x^2+3x+9/4=5+ 9/4     Factor. Fo ahead and combine the 5 and 9/4

(x+3/2)^2 = 29/4                     Square both sides.

x+3/2= the square root of 29/2     Get x by itself by subtracting 3/2

x= -3/2 plus or minus the square root of 29/2

or x= -3 + the square root of 29 all over 2