How do you solve #x^2-x-12=0#?

1 Answer
May 19, 2015

We can Split the Middle Term of this equation and factorise it to find the solution.

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

#N_1 xx N_2 = a xx c = 1 xx (-12) = -12#

and

#N_1 +N_2 = b = -1#

After trying out a few numbers we get #N_1 = -4# and #N_2 =3#
#(-4) xx 3 = -12#, and #(-4) + 3= -1#

# x^2 -x -12 = x^2 -4x +3x -12 #
#= x(x-4)+3 (x-4)#
#= (x+3)(x-4)#

the solution is #color(blue)x=-3 , color(blue)x=4#