SOLUTION: {{{x+sqrt(3x+1)=13}}}

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Question 464614: x%2Bsqrt%283x%2B1%29=13
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Transpose x to the right side:
sqrt%283x+%2B+1%29+=+13+-+x
Square both sides:
3x%2B1+=+%2813+-+x%29%5E2+=+169+-+29x+%2B+x%5E2
<==> 0+=+168+-+29x+%2B+x%5E2
<==> 0 = (21 - x)(8 - x) ==> x = 21, 8.
x = 21 is not a solution, because 21 > 13, and sqrt%283x+%2B+1%29+%3E=+0.
x = 8 satisfies the equation, and thus is the final answer.