How do you solve using the completing the square method 9x^2-12x+5=09x2−12x+5=0?

1 Answer
Gió
Mar 7, 2016

I found:
x_1=(2+i)/3x1=2+i3
x_2=(2-i)/3x2=2−i3

Explanation:

Let us manipulate a bit our expression (take the 55 to the right):
9x^2-12x=-59x2−12x=−5
let us add and subtract 44 to the left:
9x^2-12xcolor(red)(+4-4)=-59x2−12x+4−4=−5
rearrange:
9x^2-12x+4=4-59x2−12x+4=4−5
let us recognize the square on the left as:
color(blue)((3x-2)^2)=-1(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√−1=i (the immaginarty unit) and keep on going solving our equation as:
sqrt((3x-2)^2)=sqrt(-1)√(3x−2)2=√−1
3x-2=+-i3x−2=±i
so we have 2 solutions:
x_1=(2+i)/3x1=2+i3
x_2=(2-i)/3x2=2−i3

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