How do you factor #x^2 + 12x + 31# by completing the square?

1 Answer
George C.
Jun 24, 2016

Complete the square and use the difference of squares identity to find:

#x^2+12x+31=(x+6-sqrt(5))(x+6+sqrt(5))#

Explanation:

We will also use the difference of squares identity:

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

with #a=(x+6) and #b=sqrt(5)# as follows:

#x^2+12x+31#

#=x^2+2(6x)+36-5#

#=(x+6)^2-(sqrt(5))^2#

#=((x+6)-sqrt(5))((x+6)+sqrt(5))#

#=(x+6-sqrt(5))(x+6+sqrt(5))#

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