How do you solve using the completing the square method #x^2+8x+15=0#?

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Answer 1 · 2016-04-11T05:59:11

The solutions for the equation are:
#color(green)(x = - 3 # ,# color(green)(x = -5#

#x^2 + 8x + 15 = 0#

#x^2 + 8x = -15#

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

#x^2 + 8x + 16 = - 15 + 16#

#x^2 + 2 * x * 4 + 4^2 = 1 #

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

#(x+4)^2 = 1#

#x + 4 = sqrt1# or #x +4 = -sqrt 1#

#x = sqrt 1 - 4# or # x = -sqrt 1 - 4#

#x = 1 - 4# or # x = -1 - 4#

#color(green)(x = - 3 # or # color(green)(x = -5#