SOLUTION: sqrt2x+4=Sqrt(x+3)+1

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Question 62209: sqrt2x+4=Sqrt(x+3)+1
Answer by joyofmath(189) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%282x%2B4%29=sqrt%28x%2B3%29%2B1
Square both sides: 2x%2B4+=+%28x%2B3%29%2B2sqrt%28x%2B3%29%2B1.
Subtract x+4 from both sides: x+=+2sqrt%28x%2B3%29.
Square both sides: x%5E2+=+4%28x%2B3%29.
Turn the equation into a quadratic: x%5E2-4x-12+=+0.
This factors: %28x-6%29%28x%2B2%29=+0.
So, x=6 and x=-2 are possible solutions.
Let's check the possible solutions:
When x=6, sqrt%282x%2B4%29=sqrt%2816%29+=+4 and sqrt%28x%2B3%29%2B1+=+sqrt%289%29%2B1+=+4.
When x=-2, sqrt%282x%2B4%29=sqrt%280%29+=+0 and sqrt%28x%2B3%29%2B1+=+sqrt%281%29%2B1+=+2 so x= -2 is not an answer.
So, the only answer is x=6.