How do you solve using the completing the square method #x^2 - 6x - 16=0#?

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Answer 1 · 2016-03-22T17:40:01

The solutions are:
#x = 8# and
# x = -2#

#x^2 - 6x - 16=0#

#x^2 - 6x = 16#

To write the Left Hand Side as a Perfect Square, we add 9 to both sides:

#x^2 - 6x + color(blue)(9)= 16+ color(blue)(9)#

#x^2 - 2*x*3 + 3^2 = 25#

Using the Identity #color(blue)((a-b)^2 = a^2 - 2ab + b^2#, we get:

#(x-3)^2 = 25#

#x - 3 = sqrt 25# or #x -3 = -sqrt25#

#x = 5 + 3 = 8# or # x = -5 + 3 = -2#

The solutions are:
#x = 8# and
# x = -2#