How do you solve using the completing the square method # x^2 - 4x + 4 = 100#?

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Answer 1 · 2017-09-05T07:41:50

#x=12, " or "-8#

#x^2-4x+4=100#

#=>x^2+4x=100-4=96#

#x^2-4x=96#

take the coefficient of #x# half it , square it and add and subtract to #LHS#

#x^2-4x+(2)^2-(2)^2=96#

#color(red)(x^2-4x+(2)^2)-(2)^2=96#

the terms in red forma perfect square

#color(red)((x-2)^2)-4=96#

now solve for #x#

#(x-2)^2=96+4=100#

#x-2=+-sqrt100#

#x-2=+-10#

#:x=+10+2, "or "x=-10+2#

#:.x=12, " or "-8#