SOLUTION: I need help finding two consecutive odd integers the product of which is 143. i have tried the solution n(n+2)=143 is that the proper solution?

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Question 473450: I need help finding two consecutive odd integers the product of which is 143.
i have tried the solution n(n+2)=143 is that the proper solution?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
n%28n%2B2%29=143 Start with the given equation


n%5E2%2B2n=143 Distribute


n%5E2%2B2n-143=0 Subtract 143 from both sides.


Notice that the quadratic n%5E2%2B2n-143 is in the form of An%5E2%2BBn%2BC where A=1, B=2, and C=-143


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-%282%29+%2B-+sqrt%28+%282%29%5E2-4%281%29%28-143%29+%29%29%2F%282%281%29%29 Plug in A=1, B=2, and C=-143


n+=+%28-2+%2B-+sqrt%28+4-4%281%29%28-143%29+%29%29%2F%282%281%29%29 Square 2 to get 4.


n+=+%28-2+%2B-+sqrt%28+4--572+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-143%29 to get -572


n+=+%28-2+%2B-+sqrt%28+4%2B572+%29%29%2F%282%281%29%29 Rewrite sqrt%284--572%29 as sqrt%284%2B572%29


n+=+%28-2+%2B-+sqrt%28+576+%29%29%2F%282%281%29%29 Add 4 to 572 to get 576


n+=+%28-2+%2B-+sqrt%28+576+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


n+=+%28-2+%2B-+24%29%2F%282%29 Take the square root of 576 to get 24.


n+=+%28-2+%2B+24%29%2F%282%29 or n+=+%28-2+-+24%29%2F%282%29 Break up the expression.


n+=+%2822%29%2F%282%29 or n+=++%28-26%29%2F%282%29 Combine like terms.


n+=+11 or n+=+-13 Simplify.


So the solutions are n+=+11 or n+=+-13