SOLUTION: Please help me solve this radical equation. I have tried different things but just can't figure out how they got their answer. sqrrt of 3x+1=sqrrt of x The x on both sides t

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Question 34856This question is from textbook Prentice Hall Algebra
: Please help me solve this radical equation. I have tried different things but just can't figure out how they got their answer.

sqrrt of 3x+1=sqrrt of x The x on both sides throws me off. This question is from textbook Prentice Hall Algebra

Found 3 solutions by stanbon, checkley71, askmemath:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website!
sqrt(3x+1) = sqrt(x)
Square both sides of the equation to get:
3x+1=x
2x+1=0
x=-1/2
This looks like a solution but it is not.
Why?
If you substitute this back into the original equation
you get sqrt(5/2)= sqrt(-1/2), which is not true.
Why did this happen.
When you squared both sides you introduced a solution
which was extraneous to the original problem.
You original problem has NO SOLUTION.
Cheers,
Stan H.

Answer by checkley71(8403)   (Show Source):
You can put this solution on YOUR website!
SQRT3X+1=SQRTX OR SQUARING BOTH SIDES OF THE EQUATION YOU GET 3X+1=X OR
3X-X=-1 OR 2X=-1 OR X=-1/2
PROOF SQRT3(-1/2)+1=SQRT-1/2 OR SQRT-3/2+1=SQRT-1/2 OR SQRT1/2=SQRT1/2

Answer by askmemath(368)   (Show Source):
You can put this solution on YOUR website!

Squaring on both sides
3x+1 = x
2x+1 = 0
2x = -1
X = -1/2