How do you solve #x^2 + 8x = 14# by completing the square?

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Answer 1 · 2015-04-29T10:36:33

#x^2 + 8x = 14#

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

#x^2 + 8x + 16 = 14 + 16#

#x^2 + 2*4*x + 4^2 = 30#

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

#(x+4)^2 = 30#

#x + 4 = sqrt30# or #x +4 = -sqrt30#

#color(green)(x = sqrt 30 - 4# or # color(green)(x = -sqrt 30 + 4#