How do you solve #x^2 - 2x - 5 = 0#?

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Answer 1 · 2015-09-12T07:09:54

The solutions are:
#color(blue)(=1+sqrt(6)#

#color(blue)(=1-sqrt(6)#

# x^2−2x−5=0#

The equation is of the form #color(blue)(ax^2+bx+c=0# where:
#a=1, b=-2, c= -5#

The Discriminant is given by:
#Delta=b^2-4*a*c#

# = (-2)^2-(4*1* (-5))#

# = 4 +20 = 24#

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

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

#=(cancel2(1+-sqrt(6)))/cancel2#

The solutions are:
#color(blue)(=1+sqrt(6)#

#color(blue)(=1-sqrt(6)#