SOLUTION: Find the solution set for (radical 3x+7)+(radical x+6)=3.

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Question 71911: Find the solution set for (radical 3x+7)+(radical x+6)=3.
Answer by galactus(183) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%283x%2B7%29%2Bsqrt%28x%2B6%29=3
sqrt%283x%2B7%29=3-sqrt%28x%2B6%29
Square both sides and get:
3x%2B7=x%2B15-6sqrt%28x%2B6%29
Subtract x+15 from both sides and get:
2x-8=-6sqrt%28x%2B6%29
Square both sides again:
4x%5E2-32x%2B64=36x%2B216
4x%5E2-68x-152=0
Divide by 4:
x%5E2-17x-38=0
Factor:
(x-19)(x+2)=0
Only one of these is viable. The other is extraneous.
Checking in the original equation, we see x=-2 is the solution.