Question

Could someone please step me through how to answer this question? n^2 + 2/3n = -1/9

Answer 1

Add 1/9 to both sides
n^2+2/3n+1/9=0
factor
I recognize a perfect square binomial
(a+b)^2=a^2+2ab+b^2
1n^2+2(n)(1/3)+(1/3)^2
(n+1/3)^2=0
set to zero
n+1/3=0
minus 1/3
n=-1/3