SOLUTION: Sqrt(3)+ Sqrt(x-2)=Sqrt(x+3)

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Question 289126: Sqrt(3)+ Sqrt(x-2)=Sqrt(x+3)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%283%29%2Bsqrt%28x-2%29=sqrt%28x%2B3%29 Start with the given equation.


%28sqrt%283%29%2Bsqrt%28x-2%29%29%5E2=x%2B3 Square both sides (to eliminate the square root on the right side)


3%2B2%2Asqrt%283%29%2Asqrt%28x-2%29%2Bx-2=x%2B3 FOIL


3%2B2%2Asqrt%283%28x-2%29%29%2Bx-2=x%2B3 Combine the roots.


2%2Asqrt%283x-6%29%2Bx%2B1=x%2B3 Distribute


2%2Asqrt%283x-6%29=x%2B3-x-1 Subtract 'x' from both sides. Subtract 1 from both sides.


2%2Asqrt%283x-6%29=2 Combine like terms.


sqrt%283x-6%29=2%2F2 Divide both sides by 2.


sqrt%283x-6%29=1 Reduce.


3x-6=1%5E2 Square both sides (to eliminate the square root)


3x-6=1 Square 1 to get 1.


3x=1%2B6 Add 6 to both sides.


3x=7 Combine like terms.


x=7%2F3 Divide both sides by 3 to isolate 'x'.


So the solution is x=7%2F3


I'll let you do the check. Simply plug this value back into the equation and simplify. You should get an equation that is always true.