How do you solve # x^2 + 14x - 15 = 0# by completing the square?

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Answer 1 · 2016-04-04T16:30:00

The solutions are:
#color(green)(x = 1# or # color(green)(x = -15#

#x^2 + 14x - 15=0#

#x^2 + 14x = 15#

To write the Left Hand Side as a Perfect Square, we add #49 # to both sides:

#x^2 + 14x + 49 = 15 + 49 #

#x^2 + 2* x * 7 + 7^2 = 64#

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

#(x+7)^2 = 64#

#x + 7 = sqrt64# or #x +7 = -sqrt64#

#color(green)(x = 8-7 = 1# or # color(green)(x = -8 - 7 = -15#