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

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Answer 1 · 2016-04-26T14:39:19

The solutions are:
#color(green)(x = 1 , x=-9#

#x^2 + 8x = 9#

To write the Left Hand Side as a Perfect Square, we add 16 to both sides:

#x^2 + 8x + 16 = 9+ 16#

#x^2 + 2* x * 4 + 4^2 = 25#

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

#(x+4)^2 = 25#

#x + 4 = sqrt25# or #x +4 = -sqrt25#

#x + 4 = 5# , #x +4 = -5#

#x = 5- 4 =1 # ,

#x = -5 -4 = -9#

The solutions are:
#color(green)(x = 1 , x=-9#