How do you solve #4x^2-14x-8=0#?

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Answer 1 · 2015-07-08T09:32:20

The solutions for the equation are
#color(blue)(x=4, x=-1/2#

#4x^2 -14x -8 = 0#

We can first factorise the equation and then find the solutions :

Factorising by splitting the middle term:

#4x^2 -14x -8 = 0#

#4x^2 + color(blue)(2x -16x) -2 = 0#

#2x (2x+1) -8 (2x+1) = 0#

#color(blue)((2x -8)(2x+1) = 0#

Now, equating the factors with zero to obtain the solutions
#2x -8 = 0 , color(blue)(x=8/2 = 4#
#2x+1 = 0 ,color(blue)( x =-1/2#