How do you solve by completing the square: #x^2 – 4x – 60 = 0#?
2 Answers
Solving a quadratic expression by completing the square means to manipulate the expression in order to write it in the form
So, if
and conclude
Now, we have
Adding
Which is the form we wanted, because now we have
Which leads us to

First, we Transpose the Constant to one side of the equation.
Transposing#60# to the other side we get:
#x^24x = 60# 
Application of
#(ab)^2 = a^2  2ab + b^2#
We look at the Coefficient of#x# . 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.
#x^24x+4 = 60+4#
#x^24x+4 = 64#
The Left Hand side#x^24x+4# is in the form#a^2  2ab + b^2#
where#a# is#x# , and#b# is#2# 
The equation can be written as
#(x2)^2 = 64#
So

Solution :
#x = 10,6# 
Verify your answer by substituting these values in the Original Equation
#x^2 4x  60 = 0#
The Left hand Side is#x^2 4x  60# , and the Right Hand Side is#0#
If x = 10,
Left Hand Side
If x = 6,
Left Hand Side
Both the solutions are verified. Our solution