How do you solve #6x^2+5x+1=0#?

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Answer 1 · 2015-07-12T16:28:46

The solutions are:
#color(blue)(x=-1/2,x=-1/3#

#6x^2 +5x+1 =0#
We can first factorise the expression and then find the solutions.

Factorising by splitting the middle term

#6x^2 +color(blue)(5x)+1 =0#

#6x^2 color(blue)(+2x +3x)+1 =0#

#2x(3x+1) +1(3x+1) =0#

#(2x+1)(3x+1) =0#

Now we equate the factors with zero to obtain the solutions:

#2x+1 =0, color(blue)(x=-1/2#

#3x+1=0, color(blue)(x=-1/3#