How do you solve #x^2-4x-2=0# by using the Quadratic Formula?

1 Answer
Jul 25, 2015

Answer:

The solutions are:
#color(blue)(x=2+sqrt6#
#color(blue)(x=2-sqrt6#

Explanation:

The equation: #x^2-4x-2# is of the form #color(blue)(ax^2+bx+c=0# where:
#a=1, b=-4, c=-2#

The Discriminant is given by:

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

# = (-4)^2 - (4)* (1)*(-2)#
# = 16+8=24#

As #Delta>0# there are two solutions,

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

#x = (-(-4)+-sqrt(24))/(2*1) = (4+-sqrt(24))/2#

#(color(blue)(sqrt24 = sqrt(2*2*2*3) = 2sqrt6)#

So,
# x= (4+-2sqrt(6))/2#

Taking #2 # outside the bracket as it is common to both terms of the numerator

# x= (cancel2(2+-sqrt(6)))/cancel2#
the solutions are:
#color(blue)(x=2+sqrt6#
#color(blue)(x=2-sqrt6#