SOLUTION: Square root 3x+3 plus square root x+2 = 5

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Question 870637: Square root 3x+3 plus square root x+2 = 5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%283x%2B3%29%2Bsqrt%28x%2B2%29+=+5


sqrt%283x%2B3%29+=+5-sqrt%28x%2B2%29


%28sqrt%283x%2B3%29%29%5E2+=+%285-sqrt%28x%2B2%29%29%5E2


3x%2B3+=+%285-sqrt%28x%2B2%29%29%5E2


3x%2B3+=+25-10%2Asqrt%28x%2B2%29%2Bx%2B2


3x%2B3+=+27-10%2Asqrt%28x%2B2%29%2Bx


3x%2B3-27-x=-10%2Asqrt%28x%2B2%29


2x-24=-10%2Asqrt%28x%2B2%29


%282x-24%29%5E2=%28-10%2Asqrt%28x%2B2%29%29%5E2


4x%5E2-96x%2B576=100%28x%2B2%29


4x%5E2-96x%2B576=100x%2B200


4x%5E2-96x%2B576-100x-200=0


4x%5E2-196x%2B376=0


4%28x%5E2-49x%2B94%29=0


x%5E2-49x%2B94=0%2F4


x%5E2-49x%2B94=0


%28x-47%29%28x-2%29=0


x-47=0 or x-2=0


x=47 or x=2


The *possible* answers are x=47 or x=2


We need to check them.


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Checking x=47


sqrt%283x%2B3%29%2Bsqrt%28x%2B2%29+=+5


sqrt%283%2A47%2B3%29%2Bsqrt%2847%2B2%29+=+5


sqrt%28141%2B3%29%2Bsqrt%2847%2B2%29+=+5


sqrt%28144%29%2Bsqrt%2849%29+=+5


12%2B7+=+5


19+=+5 This is FALSE. So x=47 is NOT a solution.


Checking x=2


sqrt%283x%2B3%29%2Bsqrt%28x%2B2%29+=+5


sqrt%283%2A2%2B3%29%2Bsqrt%282%2B2%29+=+5


sqrt%286%2B3%29%2Bsqrt%282%2B2%29+=+5


sqrt%289%29%2Bsqrt%284%29+=+5


3%2B2+=+5


5+=+5 This is TRUE. So x=2 is a solution.


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Final Answer: x=2