SOLUTION: If 2 times a number is decreased by 9, the principal square root of this difference is 6 less than the number. Find the numbers (s)

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Question 1171541: If 2 times a number is decreased by 9, the principal square root of this difference is 6 less than the number. Find the numbers (s)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
If 2 times a number is decreased by 9, the principal square root of this difference is 6 less than the number.
Find the numbers (s)
:
The way I see this
sqrt%282n-9%29+=+n+-+6
square both sides
2n+-+9+=+%28n-6%29%5E2
FOIL (n-6)(n-6)
2n+-+9+=+n%5E2+-+12n+%2B+36
combine like terms on the right
0+=+n%5E2+-+12n+-+2n+%2B+36+%2B+9
a quadratic equation
n%5E2+-+14n+%2B+45+=+0
Factors to
(n-5)(n-9) = 0
Two solutions
n = 5
n = 9
Check both in the original equation
sqrt%282%285%29-9%29+=+5+-+6
sqrt%2810-9%29+=+5+-+6
sqrt%281%29+=+-1
and
sqrt%282%289%29-9%29+=+9+-+6
sqrt%289%29+=+3
I think the only real solution is n=9