How do you solve # x^2 - 6x - 3 = 0 #?

1 Answer
Aug 31, 2016

Answer:

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

Explanation:

Complete the square then use the difference of squares identity:

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

with #a=(x-3)# and #b=2sqrt(3)# as follows:

#0 = x^2-6x-3#

#color(white)(0) = x^2-6x+9-12#

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

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

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

Hence:

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