How do you solve #5x^2 - 2x – 2 = 0#?

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Answer 1 · 2015-08-12T06:17:56

The solutions are:

#color(blue)(x= (1+sqrt11)/5#

#color(blue)(x= (1-sqrt11)/5#

#5x^2−2x – 2=0#

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

The Discriminant is given by:

#color(blue)(Delta=b^2-4*a*c#

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

#=4+40#

# = 44#

The solutions are found using the formula:

#color(blue)(x=(-b+-sqrtDelta)/(2*a)#

#x = (-(-2)+-sqrt(44))/(2*5) = (2+-2sqrt(11))/10#

#=(cancel2(1+-sqrt11))/cancel10 = (1+-sqrt11)/5#

The solutions are:

#color(blue)(x= (1+sqrt11)/5#

#color(blue)(x= (1-sqrt11)/5#