SOLUTION: solve the quadratic equation by using the COMPLETING THE SQUARE method and applying the square root property. {{{n^2-2/3n=1/9}}}

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Question 331424: solve the quadratic equation by using the COMPLETING THE SQUARE method and applying the square root property.
n%5E2-2%2F3n=1%2F9
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the quadratic equation by using the COMPLETING THE SQUARE method and
applying the square root property.
;
I think the problem should be:
n%5E2-%282%2F3%29n+=+1%2F9
:
n%5E2-%282%2F3%29n+%2B+____+=+1%2F9
:
%281%2F3%29%5E2 = 1%2F9completes the square
n%5E2-%282%2F3%29n+%2B+1%2F9 = 1%2F9+%2B+1%2F9
n%5E2-%282%2F3%29n+%2B+1%2F9 = 2%2F9
%28n-1%2F3%29%5E2 = 2%2F9
Find the square root of both sides
n-1%2F3 = +/-sqrt%282%2F9%29
Extract 1/3 from 1/9
n-1%2F3 = +/-sqrt%282%29%2F3
n = 1%2F3+/-sqrt%282%29%2F3
Two solutions
n = %281+%2B+sqrt%282%29%29%2F3
and
n = %281+-+sqrt%282%29%29%2F3
:
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One way to check this problem:
Use a cal, find that the approx decimal value for %281+%2B+sqrt%282%29%29%2F3 = .8047
Substitute this value for n in the original problem find the value
.8047^2 -2%2F3(.8047) = .111 which is the decimal value of 1/9, ,1111
confirms our solution, you can do the same with %281+-+sqrt%282%29%29%2F3