How do you solve #x^2 − 8x − 4 = 0# using the quadratic formula?

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Answer 1 · 2015-08-10T07:32:04

The solutions for the equation are:
#color(blue)(x=4+2sqrt5 #
# color(blue)(x=4-2sqrt5#

# x^2−8x−4=0#

The equation is of the form #color(blue)(ax^2+bx+c=0# where:
#a=1, b=-8, c=-4#

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

# = (-8)^2-(4*(1)*-4)#

# = 64+16#

#=80#

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

#x = (-(-8)+-sqrt(80))/(2*1) = (8+-4sqrt(5))/2#

# x=(cancel2(4+-2sqrt(5)))/cancel2#

#x=4+-2sqrt5#

The solutions are
#color(blue)(x=4+2sqrt5 , color(blue)(x=4-2sqrt5#