SOLUTION: solve for x: the square root of x + 7 = x - 5.

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Question 377675: solve for x: the square root of x + 7 = x - 5.
Found 2 solutions by Fombitz, stanbon:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Square both sides,
x%2B7=%28x-5%29%5E2
x%2B7=x%5E2-10x%2B25
x%5E2-11x%2B18=0
Factor,
%28x-2%29%28x-9%29=0
Two solutions:
x-2=0
highlight%28x=2%29%29
.
.
.
x-9=0
highlight%28x=9%29

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
solve for x: the square root of x + 7 = x - 5.
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sqrt(x+7) = x-5
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Square both sides to get:
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x+7 = x^2-10x+25
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Simplify:
x^2 -11x + 18 = 0
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(x-9)(x-2) = 0
----
x = 9 or x = 2
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Check for extraneous roots:
sqrt(9+7) = 9-5
true
----
sqrt(2+7) = 2-5
false, therefore x=2 is extraneous
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Solution: x = 9
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Cheers,
Stan H.