SOLUTION: Solve for n when n^2 + 5n + 18 = 7363094 assuming n is an integer 0 <= n <= 10000

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Question 1083093: Solve for n when n^2 + 5n + 18 = 7363094 assuming n is an integer 0 <= n <= 10000
Found 2 solutions by math_helper, natolino_2017:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
+n%5E2+%2B+5n+%2B+18+=+7363094+
+n%5E2+%2B+5n+++++++++=+7363076+
Complete the square:
+n%5E2+%2B+5n+%2B+25%2F4+=+7363076+%2B+25%2F4+
+%28n%2B5%2F2%29%5E2+=+28452329%2F4+
+++n%2B5%2F2+=+sqrt%28+28452329%2F4%29+
+++n%2B5%2F2+=+5427%2F2+
+++n+=+5422%2F2+=+highlight%282711%29+
—
Check: +2711%5E2+%2B+5%2A2711+%2B+18+=+7349521+%2B+13555+%2B+18+=+7363094+ (ok)

Answer by natolino_2017(77) About Me  (Show Source):
You can put this solution on YOUR website!
n^2 + 5n + 18 = 7,363,094
n^2 +5n -7,363,076 = 0
Using the fromula:
n+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
with a = 1, b = 5 and c = -7,363,076
using only the positive solution.
n+=+%28-5+%2B+sqrt%28+5%5E2-4%2A-7363076+%29%29%2F%282%29+
n+=%28-5+%2Bsqrt%2829452329%29%29%2F2+= (-5 + 5,427)/2 = 2,711.
@natolino_