SOLUTION: The sum of 6 times a positive integer & its square is 91 . find the integer

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Question 1040842: The sum of 6 times a positive integer & its square is 91 . find the integer
Found 2 solutions by ikleyn, chen.aavaz:
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
6x+%2B+x%5E2 = 91.

x%5E2+%2B+6x+-+91 = 0.

Factor left side:

(x-7)*(x+13) = 0.

===>  x = 7 or  x = -13.

Since the number is positive, only one solution remains: x = 7.

Check: 6*7 + 49 = 42 + 49 = 91.

Answer.  The number is 7.

Solved.


Answer by chen.aavaz(62) About Me  (Show Source):
You can put this solution on YOUR website!
Let the integer be x.
6%2Ax%2Bx%5E2=91
x%5E2%2B6%2Ax-91=0
The roots are:
x+=+%28-6+%2B-+sqrt%28+6%5E2-4%2A1%2A%28-91%29%29%29%2F%282%2A1%29
We keep only the positive root since the problem states that the integer is positive.
Therefore
x=7