How do you solve #f^2 - 18f + 70 = -8# by completing the square?

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Answer 1 · 2016-05-13T18:09:31

The solutions are:
#color(green)(f= sqrt 3 + 9 # , # color(green)(f = -sqrt 3 +9#

#f^2 - 18f + 70 = - 8#

#f^2 - 18f = - 78#

To write the Left Hand Side as a Perfect Square, we add 81 to both sides:

#f^2 - 18f + 81 = - 78 + 81#

#f^2 - 2 * f * 9 + 9^2 = 3#

Using the Identity #color(blue)((a-b)^2 = a^2 - 2ab + b^2#, we get
#( f - 9)^2 = 3#

#f-9 = sqrt3# or #f-9 = -sqrt3#

#color(green)(f= sqrt 3 + 9 # , # color(green)(f = -sqrt 3 +9#