How do you solve #x^2+16x=17# by completing the square?

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Answer 1 · 2016-04-13T16:16:01

#color(green)(x = 1 # , # color(green)(x = -17#

#x^2 + 16x = 17 #

To write the Left Hand Side as a Perfect Square, we add 64 to both sides:

#x^2 + 16x + 64 = 17 + 64 #

#x^2 + 2 * x * 8 + 8^2 = 81 #

Using the Identity #color(blue)((a+b)^2 = a^2 + 2ab + b^2#, we get
#(x+8)^2 = 81#

#x + 8 = sqrt81# or #x +8 = -sqrt81#

#x + 8 = 9# or #x +8 = -9#

#x = 9 - 8 =1 # or #x = -9 - 8 #

#color(green)(x = 1 # or # color(green)(x = -17#