SOLUTION: sqrt of 3x + sqrt of 12 = x+5 over sqrt of 3, please help.

SOLUTION: sqrt of 3x + sqrt of 12 = x+5 over sqrt of 3, please help.

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Question 260291: sqrt of 3x + sqrt of 12 = x+5 over sqrt of 3, please help.
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
Here is the original problem:

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I don't know if the first x is in or outside of the square root. Lets first assume in and see where it takes us.
step 1 - multiply evreything by sqrt(3) to get

step 2 - simplify the square roots to get

step 3 - subtract 6 from both sides to get

step 4 - divide by 3 to get

step 5 - square both sides to get

step 6 - multiply everything by 9 to get

step 7 - set = 0 and factor

by quadratic, we get

then

and then

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Now, suppose the x is outside the square root. We get

step 1 - multiply evreything by sqrt(3) to get

step 2 - simplify the square roots to get

step 3 - subtract x from both sides to get

step 4 - subtract 6 from both sides to get

divide by 2 to get

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