SOLUTION: solve for x: {{{ sqrt(x)-4=sqrt(9x)}}} my teacher gave me the answer, and she said it is x=4 or x=1, but i do not know how to do the work to get that. Please help!!!!!!!!!

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Question 314389: solve for x:

my teacher gave me the answer, and she said it is x=4 or x=1, but i do not know how to do the work to get that. Please help!!!!!!!!!

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
sqrt(x)-4=sqrt(9x)
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Square both sides to get:
x - 8sqrt(x) + 16 = 9x
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Simplify:
-8sqrt(x) = 8x-16
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Divide both sides by -8 to get:
sqrt(x) = 2 - x
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Square both sides:
x = 4-4x+x^2
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Rearrange:
x^2 -5x+4 = 0
Factor:
(x-4)(x-1) = 0
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Potential Answers:
x = 1 or x = 4
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Check these in the original equation:
sqrt(x)-4=sqrt(9x)
Check x=1:
sqrt(1) -4 = sqrt(9)
1-4 = 3
-3 = 3
False
So, x = 1 is not an acceptable answer.
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Check x = 4:
sqrt(4) - 4 = sqrt(9*4)
2 -4 = 6
-2 = 6
False
So, x = 4 is not an acceptable answer.
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Conclusion: The original equation has no solutions.
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Cheers,
Stan H.