SOLUTION: Hi... may I have help with this question? I don't know how to write it into an equation. "A positive integer number increased by its square is equal to 81 times the next higher

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hi... may I have help with this question? I don't know how to write it into an equation. "A positive integer number increased by its square is equal to 81 times the next higher       Log On


   

Question 1106017: Hi... may I have help with this question? I don't know how to write it into an equation.
"A positive integer number increased by its square is equal to 81 times the next higher positive integer number. Find the number."
Thank you.
Found 3 solutions by josgarithmetic, stanbon, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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A positive integer number increased by its square
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n%2Bn%5E2


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is equal to 81 times the next higher positive integer number.
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previousdescription=81%28n%2B1%29



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Find the number.
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highlight_green%28n%2Bn%5E2=81%28n%2B1%29%29

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factorize left side,
n%281%2Bn%29=81%28n%2B1%29
n%28n%2B1%29=81%28n%2B1%29
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highlight%28n=81%29

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A positive integer number increased by its square is equal to 81 times the next higher positive integer number. Find the number.
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Equation::
x + x^2 = 81(x+1)
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x + x^2 = 81x + 81
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x^2 -80x - 81 = 0
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Factor::
(x-81)(x+1) = 0
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Positive solution::
x = 81
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Cheers,
Stan H.
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Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
It even can be solved WITHOUT solving the quadratic equation:


n + n^2 = 81*(n+1)  ====>


n*(n+1) = 81(*(n+1)  ====>  cancel (n+1) in both sides  ====>

n = 81.

Solved.