<PRE><B>Question 778082</B>
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 - {{{sqrt(n)}}} = 42
subtract 12 from both sides
n - {{{sqrt(n)}}} = 30
we can also write it:
n - 30 = {{{sqrt(n)}}}
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 - {{{sqrt(36)}}} = 42
48 - 6 = 42, OK
:
do the same with n=25
25 + 12 - {{{sqrt(25)}}} = 42
37 - 5 does not equal 42, so n=25 if not a solution</PRE>