How do you solve #x²-6x+3=0# using the quadratic formula?

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Answer 1 · 2016-06-28T18:40:52

The solutions are:
#color(blue)( x = 3 + sqrt6#

#color(blue)( x = 3 - sqrt6#

#x^2 - 6x +3 = 0 #

The equation is of the form #color(blue)(ax^2+bx+c=0# where:
#a=1, b=-6, c=3#

The Discriminant is given by:

#Delta=b^2-4*a*c#

# = (-6)^2-(4* 1 * 3)#

# = 36 - 12= 24 #

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

#x = (-(-6)+-sqrt(24))/(2*1) = (6+-sqrt(24))/2#

#sqrt24# can be further simplified as follows:

#sqrt24 = sqrt ( 2 * 2 * 2 * 3) = sqrt ( 2 ^2 * 2 * 3 ) = 2 sqrt6#

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

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

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

The solutions are:
#color(blue)( x = 3 + sqrt6#
#color(blue)( x = 3 - sqrt6#