SOLUTION: Sqrt(5x+1)-sqrt(x)=5

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Question 874864: Sqrt(5x+1)-sqrt(x)=5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%285x%2B1%29-sqrt%28x%29=5


sqrt%285x%2B1%29=5%2Bsqrt%28x%29


%28sqrt%285x%2B1%29%29%5E2=%285%2Bsqrt%28x%29%29%5E2


5x%2B1=%285%2Bsqrt%28x%29%29%5E2


5x%2B1=25%2B10%2Asqrt%28x%29%2Bx


5x%2B1-25-x=10%2Asqrt%28x%29


4x-24=10%2Asqrt%28x%29


%284x-24%29%5E2=%2810%2Asqrt%28x%29%29%5E2


%284x-24%29%5E2=100x


16x%5E2-192x%2B576=100x


16x%5E2-192x%2B576-100x=0


16x%5E2-292x%2B576=0


4%284x-9%29%28x-16%29=0


4x-9=0 or x-16=0


x=9%2F4 or x=16


The *possible* solutions are x=9%2F4 or x=16


However, you'll find that plugging x=9%2F4 back into sqrt%285x%2B1%29-sqrt%28x%29=5 results in a false equation (I'll let you do that part).


Plugging x=16 into sqrt%285x%2B1%29-sqrt%28x%29=5 results in a true equation (I'll let you do that part as well).


So that means x=16 is the only solution.