Algebra/derive

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Question
(ax)squared+bx+c=0 drive to get




-b+ square root of b + 4ac
 -
all over 2a  

Answer
re-write it as x^2 +(b/a)x = -c/a
complete the square by adding [b/(2a)]^2 to each side to get
x^2 +(b/a)x +b^2/(4a^2) = b^2/(4a^2) -c/a
[x +b/(2a)]^2 = (b^2 -4ac)/(4a^2)
taking the square root of each side
x +b/(2a) = +/- (b^2-4ac)^1/2/2a
x = [-b +/- (b^2-4ac)^1/2]/(2a)

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