SOLUTION: Please help me solve this equation {{{ sqrt (3x+4)=2+ sqrt (x)}}}

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Question 597322: Please help me solve this equation +sqrt+%283x%2B4%29=2%2B+sqrt+%28x%29
Found 2 solutions by unlockmath, MathTherapy:
Answer by unlockmath(1688) About Me  (Show Source):
You can put this solution on YOUR website!
Hello,
This +sqrt+%283x%2B4%29=2%2B+sqrt+%28x%29 can be squared on both sides to get:
3x+4=(2+ sqrt x)^2
Expand this out to:
3x+4=4+4 sqrt x +x
Subtract 4 and x to get:
2x=4 sqrt x
Divide by 4 each side:
1/2(x)=sqrt x
Square both sides again to get:
1/4x^2=x
Divide by x:
1/4x=1
Multiply by 4:
x=4
Make sense?
RJ
www.math-unlock.com

Answer by MathTherapy(10801) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me solve this equation +sqrt+%283x%2B4%29=2%2B+sqrt+%28x%29
*****************************************************************
There ISN'T just 1 value for x, as the other person indicates!

    sqrt%283x+%2B+4%29+=+2+%2B+sqrt%28x%29
 %28sqrt%283x+%2B+4%29%29%5E2+=+%282+%2B+sqrt%28x%29%29%5E2 ---- Squaring each side
     3x+%2B+4+=+4+%2B+4sqrt%28x%29+%2B+x
3x+%2B+4+-+4+-+x+=+4sqrt%28x%29
        2x+=+4sqrt%28x%29
      %282x%29%5E2+=+%284sqrt%28x%29%29%5E2 ------ Squaring each side
       4x%5E2+=+16%28x%29 
  4x%5E2+-+16x+=+0
   4x%28x+-+4%29+=+0 
        4x = 0      OR     x - 4 = 0
        x = 0      OR        x = 4

Both solutions are VALID!!