How do you solve #x^2=12x-27#?

1 Answer
May 23, 2015

#x^2=12x-27#
#x^2 -12x+27=0#

We can Split the Middle Term of this expression to factorise it and thereby find the solution.
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 = 1*27 = 27#
And
N_1 +N_2 = b = -12#

After trying out a few numbers we get #N_1 = -9# and #N_2 =-3#
#9*3 = 27#, and #-9+(-3)= -12#

#x^2 -12x+27= x^2 -9x - 3x +27#
#x(x - 9) - 3(x-9) = 0#

#color(green)((x-9)(x - 3)# is the factorised form.
and #color(green)(x=9 and x=3# are the solutions.