SOLUTION: solving a polynomial equation 2/9=8n^2

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Question 189895: solving a polynomial equation
2/9=8n^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2%2F9=8n%5E2 Start with the given equation.


2=9%288n%5E2%29 Multiply both sides by 9.


2=72n%5E2 Multiply


0=72n%5E2-2 Subtract 2 from both sides.


Notice we have a quadratic equation in the form of an%5E2%2Bbn%2Bc where a=72, b=0, and c=-2


Let's use the quadratic formula to solve for n


n+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


n+=+%280+%2B-+sqrt%28+%280%29%5E2-4%2872%29%28-2%29+%29%29%2F%282%2872%29%29 Plug in a=72, b=0, and c=-2


n+=+%280+%2B-+sqrt%28+0-4%2872%29%28-2%29+%29%29%2F%282%2872%29%29 Square 0 to get 0.


n+=+%280+%2B-+sqrt%28+0--576+%29%29%2F%282%2872%29%29 Multiply 4%2872%29%28-2%29 to get -576


n+=+%280+%2B-+sqrt%28+0%2B576+%29%29%2F%282%2872%29%29 Rewrite sqrt%280--576%29 as sqrt%280%2B576%29


n+=+%280+%2B-+sqrt%28+576+%29%29%2F%282%2872%29%29 Add 0 to 576 to get 576


n+=+%280+%2B-+sqrt%28+576+%29%29%2F%28144%29 Multiply 2 and 72 to get 144.


n+=+%280+%2B-+24%29%2F%28144%29 Take the square root of 576 to get 24.


n+=+%280+%2B+24%29%2F%28144%29 or n+=+%28-0+-+24%29%2F%28144%29 Break up the expression.


n+=+%2824%29%2F%28144%29 or n+=++%28-24%29%2F%28144%29 Combine like terms.


n+=+1%2F6 or n+=+-1%2F6 Simplify.


So the answers are n+=+1%2F6 or n+=+-1%2F6