Short description: In mathematics, completing the square is generally used for solving quadratic equations or to change the quadratic expression into a desired form.
It changes the general quad. eqn. ax^2+bx+c = 0 into d(x+e)^2+f = 0
(where a,b,c,d,e,f are constants)

How it works:
Start with: ax^2+bx+c = 0
Factor out ‘a’ to get:
a(x^2+(b/a)x)+c=0 [notice you don’t factor out the a from c]
Now we add ‘0’ inside the brackets:
a(x^2+(b/a)x+(b/(2a))^2-(b/(2a))^2)+c=0
a(x^2+(b/a)x+(b/(2a))^2)-a(b/(2a))^2+c=0[notice you multiply a to -(b/(2a))^2 to take it outside the brackets]
And now factorise:
a(x+(b/(2a)))^2+c-a(b/(2a))^2=0
And we’re done.

Example:
Complete the square of this equation: 2x^2+3x-4=0
Solution:
2(x^2+(3/2)x)-4=0
2(x^2+(3/2)x+(3/4)^2-(3/4)^2)-4=0
2(x^2+(3/2)x+(3/4)^2)-2(3/4)^2-4=0
2(x+3/4)^2-9/8-4=0
2(x+3/4)^2-41/8=0
Now we can solve for x:
2(x+3/4)^2=41/8
x+3/4=(41/16)^0.5
x=(41/16)^0.5-3/4
x=0.8507…