# How do you solve #x^2-6x-9=0# by completing the square?

##### 2 Answers

Jan 19, 2018

#### Explanation:

Jan 19, 2018

#### Explanation:

The difference of squares identity can be written:

#A^2-B^2 = (A-B)(A+B)#

Use this with

#0 = x^2-6x-9#

#color(white)(0) = x^2-2(x)(3)+3^2-18#

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

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

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

Hence:

#x = 3+-3sqrt(2)#