How do you solve #x^2 - 6x = 391# by completing the square?

1 Answer
Apr 12, 2016

Answer:

#x=23# or #x-17#

Explanation:

In #x^2-6x=391# as the Left Hand Side is #x^2-6x#, we can make it a complete square (compare it with #(x-a)^2=x^2-2ax+a^2#) by adding **square of half the coefficient of #x#.

As coefficient of #x# is #-6#, we need to add #(-6/2)^2=9#, to each side and then we have

#x^2-6x+9=391+9=400#

or #(x-3)^2=20^2#

Hence either #x-3=20# or #x-3=-20# i.e.

#x=23# or #x-17#