How do you solve #2x^2 + x - 1=0# by factoring?

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Answer 1 · 2015-08-17T06:29:28

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

#2x^2+x−1=0#

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like #ax^2 + bx + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 2*-1 = -2#
AND
#N_1 +N_2 = b = 1#

After trying out a few numbers we get #N_1 = 2# and #N_2 =-1#
#2*-1 = -2#, and #2+(-1)= 1#

#2x^2+x−1=2x^2+2x-1x−1#

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

#(2x-1)(x+1)=0#
Now we equate the factors to zero
#2x-1=0, color(blue)(x=1/2#
#x+1=0, color(blue)(x=-1#