How do you solve the equation #x^2+6x+13=0# by completing the square?

1 Answer
Jan 8, 2017

Answer:

#x = -3+-2i#

Explanation:

The difference of squares identity can be written:

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

Use this with #a=(x+3)# and #b=2i# as follows:

#0 = x^2+6x+13#

#color(white)(0) = x^2+6x+9+4#

#color(white)(0) = (x+3)^2-(2i)^2#

#color(white)(0) = ((x+3)-2i)((x+3)+2i)#

#color(white)(0) = (x+3-2i)(x+3+2i)#

Hence:

#x = -3+-2i#