Given
#color(white)("XXX")x^2-8x+7=0color(white)("XX")#Note: I modified the question to include the #color(blue)(=0)#
Then
#color(white)("XXX")x^2-8x=-7#
Remembering the general relation:
#color(white)("XXX")x^2+2ax+a^2 = (x+a)^2#
If #x^2-8x# are to be the first two terms of #x^2+2ax+a^2#
then
#color(white)("XXX")a=-4#
and
#color(white)("XXX")a^2=16#
So we will need to add #16# (to both sides) to #underline("complete the square")#
#color(white)("XXX")x^2-8x+16 = -7+16#
#color(white)("XXX")(x-4)^2=9#
#color(white)("XXX")x-4=+-3#
#color(white)("XXX")x=4+-3#
#color(white)("XXX")x=7color(white)("XX")orcolor(white)("XX")x=1#
