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

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Answer 1 · 2016-03-30T16:27:48

The solutions are :
#color(green)(x = 5# or # color(green)(x = 3#

#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 = -sqrt1#

#color(green)(x = 1 + 4 = 5# or # color(green)(x = - 1 + 4 = 3#