How do you solve #x^2 - 6x + 6 = 0#?

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Answer 1 · 2015-08-02T06:27:47

The solutions are:
#color(blue)(x=3+sqrt(3)#
#color(blue)(x=3-sqrt(3)#

#x^2-6x+6#

The equation is of the form #color(blue)(ax^2+bx+c=0# where:
#a=1, b=-6, c=6#

The Discriminant is given by:
#Delta=b^2-4*a*c#
# = (-6)^2-(4*(1)*6)#
# = 36-24 = 12#

As #Delta>0# there are two solutions.

The solutions are found using the formula:
#x=(-b+-sqrtDelta)/(2*a)#

#x = (-(-6)+-sqrt(12))/(2*1) = (6+-sqrt(12))/2#

#sqrt12=sqrt(2*2*3) = 2sqrt3#

#x=(6+-2sqrt(3))/2#
#x=(cancel2(3+-sqrt(3)))/cancel2#
#x=3+-sqrt(3)#

The solutions are:
#color(blue)(x=3+sqrt(3)#
#color(blue)(x=3-sqrt(3)#