How do you solve the quadratic equation by completing the square: #x^2 -12x-2=0#?

1 Answer
Jul 13, 2015

Answer:

#x= 6+sqrt(38)# or #x=6-sqrt(38)#
#color(white)("XXXX")#(using the completing the squares method)

Explanation:

Given #x^2-12x-2 = 0#

Completing the square is simpler if we move the constant to the right side:
#color(white)("XXXX")##x^2-12x = 2#

If #x^2# and #-12x# are the first two terms of a squared binomial expansion:
#color(white)("XXXX")##(x-a)^2 = (x^2-2ax+a^2)#
then
#color(white)("XXXX")##a=6#
and
we need to add #a^2 = 36# to both sides to complete the square

#color(white)("XXXX")##x^2-12x+36 = 2+36#

Rewriting as a squared binomial (and simplifying the right side)
#color(white)("XXXX")##(x-6)^2 = 38#

Taking the square root of both sides
#color(white)("XXXX")##x-6 = +-sqrt(38)#

Adding #6# to both sides:
#color(white)("XXXX")##x=6+-sqrt(38)#