SOLUTION: √(X-2)= 5-√(X+3)

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Question 75443: √(X-2)= 5-√(X+3)
Answer by funmath(2873) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28x-2%29=5-sqrt%28x%2B3%29
%28sqrt%28x-2%29%29%5E2=%285-sqrt%28x%2B3%29%29%5E2
x-2=%285-sqrt%28x%2B3%29%29%285-sqrt%28x%2B3%29%29
x-2=5%285%29%2B5%28-sqrt%28x%2B3%29%29-sqrt%28x%2B3%29%285%29-sqrt%28x%2B3%29%28-sqrt%28x%2B3%29%29
x-2=25-5sqrt%28x%2B3%29-5sqrt%28x%2B3%29%2B%28sqrt%28x%2B3%29%29%5E2
x-2=25-10sqrt%28x%2B3%29%2B%28x%2B3%29
x-2=-10sqrt%28x%2B3%29%2Bx%2B28
x-x-2-28=-10sqrt%28x%2B3%29%2Bx-x%2B28-28
-30=-10sqrt%28x%2B3%29
-30%2F-10=-10sqrt%28x%2B3%29%2F-10
3=sqrt%28x%2B3%29
3%5E2=%28sqrt%28x%2B3%29%29%5E2
9=x%2B3
9-3=x%2B3-3
6=x
Check to make sure this solution isn't extraneous by plugging it back into the original equation and see if both sides equal.
sqrt%286-2%29=5-sqrt%286%2B3%29
sqrt%284%29=5-sqrt%289%29
2=5-3
2=2
The solution highlight%28x=6%29 is valid.
Happy Calculating!!!!