How do you solve using the completing the square method # x^2+8x=9#?

1 Answer
Feb 28, 2016

Answer:

#x=1# or #x=9#
(see below for method of completing the square).

Explanation:

A general squared binomial has the relation:
#color(white)("XXX")(a+b)^2=a^2+2ab+b^2#

If #x^2+8x# are the first two terms of an expanded squared binomial
then #a=1# and #b=4#
and the third term needed to complete the square would be #b^2=16#.

If we add #16# to the left side to complete the square there
we will need to add #16# to the right side to maintain the equality.
#color(white)("XXX")x^2+8x+16=9+16#

Re-writing the left side as a squared binomial and simplifying the right side:
#color(white)("XXX")(x+4)^2=25#

If we take the square root of both sides:
#color(white)("XXX")(x+4)=+-5#

which implies:
either #x=1# or #x=-9#