SOLUTION: The square root of a number is subtracted from the sum of the number and 12. The result is 42. What is the original number?

Question 778082: The square root of a number is subtracted from the sum of the number and 12. The result is 42. What is the original number?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The square root of a number is subtracted from the sum of the number and 12.
The result is 42. What is the original number?
:
Just write an equation for what it says:
n + 12 - = 42
subtract 12 from both sides
n - = 30
we can also write it:
n - 30 =
Square both sides
n^2 - 60n + 900 = n
Arrange as a quadratic equation
n^2 - 60n - n + 900 = 0
n^2 - 61n + 900 = 0
Factors to
(n-25)(n-36) = 0
Two solutions
n = 25
and
n = 36
:
See if n=36 works
36 + 12 - = 42
48 - 6 = 42, OK
:
do the same with n=25
25 + 12 - = 42
37 - 5 does not equal 42, so n=25 if not a solution
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