How do you solve using completing the square method #m^2+4m+2=0#?

1 Answer
George C.
Oct 5, 2016

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

Explanation:

The difference of squares identity can be written:

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

Use this with #a=(m+2)# and #b=sqrt(2)# as follows:

#0 = m^2+4m+2#

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

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

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

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

Hence:

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

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