SOLUTION: Solve √(3x+1)= 7- √(x-4). Thanks for your help.

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Question 177007: Solve √(3x+1)= 7- √(x-4). Thanks for your help.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
√(3x+1)= 7- √(x-4
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Square both sides to get:
3x+1 = 49 -14sqrt(x-4) + (x-4)
2x + 5 - 49 = -14sqrt(x-4)
2x-44 = -14sqrt(x-4)
x - 22 = -7sqrt(x-4)
Square both sides to get:
x^2 - 44x + 484 = 49(x-4)
x^2 - 44x + 484 = 49x - 196
x^2 - 93x + 680 = 0
(x-8)(x-85) = 0
x = 8 or x = 85
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Checking:√(3x+1)= 7- √(x-4
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Does x = 8 ?
sqrt(25) = 7 - sqrt(4)
5 = 7-2
Correct
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Does x = 85
sqrt(256) = 7 - sqrt(81)
16 = 7 - 9
16 = -2
False
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Only solution:
x = 8
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Cheers,
Stan H.
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