How do you solve using the completing the square method #x^2+8x=20#?

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Answer 1 · 2016-03-09T14:00:24

The solutions are:
#x = 2# ,
# x = -10#

#x^2 +8x=20#

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

#x^2 + 8x + 16 = 20 + 16#

#x^2 + 2*4*x + 4^2 = 36#

Using the Identity #color(blue)((a+b)^2 = a^2 + 2ab + b^2#, we get
#(x+4)^2 = 36#

#x + 4 = sqrt36# or #x +4 = -sqrt36#

#x = 6 - 4# or # x = -6 -4#

#x = 2# or # x = -10#

The solutions are:
#x = 2# ,
# x = -10#