How do you solve the equation #x^2+4x+2=0# by completing the square?

1 Answer
Jan 11, 2017

Answer:

#x = -2+-sqrt(2)#

Explanation:

The difference of squares identity can be written:

#a_2-b^2 = (a-b)(a+b)#

Complete the square then use this with #a=(x+2)# and #b=sqrt(2)# as follows:

#0 = x^2+4x+2#

#color(white)(0) = x^2+4x+4-2#

#color(white)(0) = (x+2)^2-(sqrt(2))^2#

#color(white)(0) = ((x+2)-sqrt(2))((x+2)+sqrt(2))#

#color(white)(0) = (x+2-sqrt(2))(x+2+sqrt(2))#

Hence:

#x = -2+-sqrt(2)#