How do you solve by completing the square: #c²36= 4c#?
1 Answer

First, we Transpose the Constant to one side of the equation.
Transposing#36# to the other side we get:
#c^2+4c = 36# 
Application of
#(a+b)^2 = a^2 + 2ab + b^2#
We look at the Coefficient of#c# . It's#4#
We take half of this number (including the sign), giving us#2#
We square this value to get#(2)^2 = 4# . We add this number to BOTH sides of the Equation.
#c^2+4c+4 = 36+4#
#c^2+4c+4 = 40#
The Left Hand side#c^2+4c+4# is in the form#a^2 + 2ab + b^2#
where#a# is#c# , and#b# is#2# 
The equation can be written as
#(c+2)^2 = 40#
So

Solution :
#c = 2(sqrt101) , 2(sqrt10+1) # 
Verify your answer by substituting these values in the Original Equation
#c^2 36 = 4c# . You will see that the solution is correct.