SOLUTION: n2+9=6n

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Question 184838: n2+9=6n
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

n%5E2%2B9=6n Start with the given equation.


n%5E2%2B9-6n=0 Subtract 6n from both sides.


n%5E2-6n%2B9=0 Rearrange the terms.


Notice we have a quadratic equation in the form of an%5E2%2Bbn%2Bc where a=1, b=-6, and c=9


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+=+%28-%28-6%29+%2B-+sqrt%28+%28-6%29%5E2-4%281%29%289%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-6, and c=9


n+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%281%29%289%29+%29%29%2F%282%281%29%29 Negate -6 to get 6.


n+=+%286+%2B-+sqrt%28+36-4%281%29%289%29+%29%29%2F%282%281%29%29 Square -6 to get 36.


n+=+%286+%2B-+sqrt%28+36-36+%29%29%2F%282%281%29%29 Multiply 4%281%29%289%29 to get 36


n+=+%286+%2B-+sqrt%28+0+%29%29%2F%282%281%29%29 Subtract 36 from 36 to get 0


n+=+%286+%2B-+sqrt%28+0+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


n+=+%286+%2B-+0%29%2F%282%29 Take the square root of 0 to get 0.


n+=+%286+%2B+0%29%2F%282%29 or n+=+%286+-+0%29%2F%282%29 Break up the expression.


n+=+%286%29%2F%282%29 or n+=++%286%29%2F%282%29 Combine like terms.


n+=+3 or n+=+3 Simplify.


So the only answer is n+=+3