SOLUTION: Solve the completing the square 6z^2=z+2

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Question 678402: Solve the completing the square
6z^2=z+2
Found 2 solutions by ReadingBoosters, mananth:
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
6z%5E2-z=2
divide the netire equation by 6
z%5E2+-+%281%2F6%29z+=+1%2F3
...

z%5E2+-+%281%2F6%29z+%2B+1%2F144+=+%281%2F3%29+%2B+%281%2F144%29
...
z%5E2+-+%281%2F6%29z+%2B+1%2F144+=+49%2F144
...
%28z-%281%2F12%29%29%5E2+=+%2849%2F144%29
...
sqrt%28z+-%281%2F12%29%29%5E2 = +/- sqrt%2849%2F144%29
...
z - 1%2F12 = +/- 7%2F12
z = %281%2F12%29+%2B-+%287%2F12%29
...
highlight_green%28z+=+8%2F12+=+2%2F3%29
AND
highlight_green%28z+=-6%2F12+=+-1%2F2%29
.....................
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Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
6z%5E2=z%2B2
6z%5E2-z=2
/6
z%5E2-%28z%2F6%29+=+1%2F3
Find the last term of perfect square
Last term = 1/2 the coefficient of 2nd. term squared
(1/2*1/6)^2
(1/12)^2= 1/144
add (1/44) to both sides
z%5E2-%28z%2F6%29+%2B%281%2F144%29+=+%281%2F3%29+%2B%281%2F144%29
%28z%2B%281%2F12%29%29%5E2=+%2848%2B1%29%2F144+ ( taking the LCD
%28z%2B%281%2F12%29%29%5E2=+49%2F144+
Take the square root of both sides
(z+(1/12)) = +/- (7/12)
z= -(1/12) +(7/12) --->1/2
OR
z= -(1/12) -(7/12) ---> -2/3