SOLUTION: sqrt(2-x) - sqrt(3x+1) = 1 When I solve this i come up with the answer 12x = 16x^2 To solve for X, do I need to divide 16X by both sides? I'm a little lost at this point.

Algebra ->  Radicals -> SOLUTION: sqrt(2-x) - sqrt(3x+1) = 1 When I solve this i come up with the answer 12x = 16x^2 To solve for X, do I need to divide 16X by both sides? I'm a little lost at this point.       Log On


   

Question 159543: sqrt(2-x) - sqrt(3x+1) = 1
When I solve this i come up with the answer 12x = 16x^2
To solve for X, do I need to divide 16X by both sides? I'm a little lost at this point.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
I didn't get to the same place.
sqrt%282-x%29+=+1+%2B+sqrt%283x%2B1%29
%282-x%29+=+1+%2B+2%2Asqrt%283x%2B1%29%2B%283x%2B1%29
%282-x%29-1-%283x%2B1%29+=+2%2Asqrt%283x%2B1%29
%282-1-1%29-x-3x=2%2Asqrt%283x%2B1%29
-4x=2%2Asqrt%283x%2B1%29
16x%5E2=4%283x%2B1%29
16x%5E2=12x%2B4
I have the additional 4.
Use the quadratic formula or factor for the solution.
16x%5E2-12x-4=0
%284x%2B1%29%284x-4%29=0
4x%2B1=0
x=-1%2F4
Check the answer
sqrt%282-x%29+-+sqrt%283x%2B1%29=1
sqrt%282%2B1%2F4%29-sqrt%283%28-1%2F4%29%2B1%29=1
1.5-0.5=1
1=1
True statement.
Good answer.
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4x-4=0
x=1
Check the answer
sqrt%282-x%29+-+sqrt%283x%2B1%29=1
sqrt%282-1%29-sqrt%283%281%29%2B1%29=1
1-2=1
-1=1
False statement.
Not a good answer.
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One solution,
x=-1%2F4
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To your question, if you were at that point,
16x%5E2=12x
Yes, divide both sides by 16x and you get,
x=12%2F16=3%2F4
But that is not a solution.