Completing the Square
Key Questions

Remember that
#(ax + b)^2 = a^2x^2 + 2abx + b^2# So the general idea to get
#b^2# is by getting#x# 's coefficient,
dividing by#2a# , and squaring the result.Example
#3x^2 + 12x# #a = 3#
#2ab = 12#
#6b = 12#
#b = 2#
#3x^2 + 12x + 4 = (3x + 2)^2# You can also factor out
#x^2# 's coefficient.. and proceed with completing the square.Example:
#2X^2 +4X# #2(X^2 + 2X)# #2(X + 1)^2# 
Answer:
#ax^2+bx+c = a(x+b/(2a))^2 + (c  b^2/(4a))# The secret is that
#b/(2a)# bitExplanation:
Suppose you are given a quadratic equation to solve:
#2x^23x2 = 0# ..which is in the form..
#ax^2+bx+c = 0# with#a = 2# ,#b=3# and#c=2# #b/(2a) = 3/4# So we find:
#2(x3/4)^2 = 2(x^2(2*x*3/4)+(3/4)^2)# #=2(x^2(3x)/2+9/16)# #=2x^23x+9/8# So:
#2(x3/4)^225/8 = 2(x3/4)^29/82# #=2x^23x+9/89/82# #=2x^23x2# So:
#2x^23x2 = 0# turns into:
#2(x3/4)^225/8 = 0# Hence:
#(x3/4)^2 = 25/16# So:
#x3/4 = +sqrt(25/16) = +5/4# and
#x = 3/4+5/4# 
Answer:
In order to use the Completing the Square method, the value for
#a# in the quadratic equation must be#1# . If it is not#1# , you will have to use the AC method or the quadratic formula in order to solve for#x# .Explanation:
Completing the square is a method used to solve a quadratic equation,
#ax^2+bx+c# , where#a# must be#1# . The goal is to force a perfect square trinomial on one side and then solving for#x# by taking the square root of both sides.The method is explained at the following website:
http://www.regentsprep.org/regents/math/algtrig/ate12/completesqlesson.htm

Completing the square is a method that represents a quadratic equation as a combination of quadrilateral used to form a square.
The basis of this method is to discover a special value that when added to both sides of the quadratic that will create a perfect square trinomial.
That special value is found by evaluation the expression
#(b/2)^2# where#b# is found in#ax^2+bx+c=0# . Also in this explanation I assume that#a# has a value of#1# .#ax^2+bx+(b/2)^2=(b/2)^2c# #(ax+b/2)^2=(b/2)^2c# #sqrt((ax+b/2)^2)=+sqrt((b/2)^2c)# #ax+b/2=+sqrt((b/2)^2c)# #ax=+sqrt((b/2)^2c)b/2# A quadratic that is a perfect square is very easy to solve.
Please take a look at the video to see an example of completing the square visually.