How do you solve the quadratic equation by completing the square: #x^2 - 6x = 16#?

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Answer 1 · 2018-03-22T11:17:50

Solution: #x=8 or x=-2#

#x^2-6x=16 or x^2-6x +9=16+9 #

#:.(x-3)^2=25 or (x-3)=+-5 #

#:.x= 3+5 or x=3-5# or

#:.x=8 or x=-2#

Solution: #x=8 or x=-2# [Ans]

Answer 2 · 2018-03-22T11:25:11

#x=8 or x=-2#

We have ,

#x^2-6x=16#

i.e. #x^2-6x+(-)=16+(-)#

To find third term, we use

#color(red)(3^(rd) term=(2^(nd) term)^2/(4xx1^(st)term)) =(-6x)^2/(4xxx^2)=(36x^2)/(4x^2)=9#

Adding both sides 9, we get

#x^2-6x+9=16+9=25#

#=>(x-3)^2=(5)^2#

Taking squareroot of both sides,

#=>x-3=+-5#

#:.x-3=5 or x-3=-5#

#:.x=8 or x=-2#