How do you solve #x^2 +8x = 7# by completing the square?

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Answer 1 · 2016-04-04T16:14:41

The solutions are:
#color(green)(x = sqrt 23 - 4# or # color(green)(x = -sqrt 23 - 4#

#x^2 + 8x = 7#

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

#x^2 + 8x + 16 = 7 + 16#

#x^2 + 2 * x * 4 + 4^2 = 23#

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

#(x+4)^2 = 23#

#x + 4 = sqrt23# or #x +4 = -sqrt23#

#color(green)(x = sqrt 23 - 4# or # color(green)(x = -sqrt 23 - 4#