How do you solve using the completing the square method #9x^2-12x+5=0#?

1 Answer
Mar 7, 2016

Answer:

I found:
#x_1=(2+i)/3#
#x_2=(2-i)/3#

Explanation:

Let us manipulate a bit our expression (take the #5# to the right):
#9x^2-12x=-5#
let us add and subtract #4# to the left:
#9x^2-12xcolor(red)(+4-4)=-5#
rearrange:
#9x^2-12x+4=4-5#
let us recognize the square on the left as:
#color(blue)((3x-2)^2)=-1#
BUT
if we try to solve taking the root of both sides we will get a negative square root!
I am not sure you know about them but we can write #sqrt(-1)=i# (the immaginarty unit) and keep on going solving our equation as:
#sqrt((3x-2)^2)=sqrt(-1)#
#3x-2=+-i#
so we have 2 solutions:
#x_1=(2+i)/3#
#x_2=(2-i)/3#