SOLUTION: sqrt(x)+ sqrt(x-5)=sqrt(2x+7)

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Question 289537: sqrt(x)+ sqrt(x-5)=sqrt(2x+7)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28x%29%2B+sqrt%28x-5%29=sqrt%282x%2B7%29
Square both sides.
%28sqrt%28x%29%2Bsqrt%28x-5%29%29%5E2=2x%2B7

x%2B2sqrt%28x%29sqrt%28x-5%29%2B%28x-5%29=2x%2B7
2x-5%2B2sqrt%28x%29sqrt%28x-5%29=2x%2B7
2sqrt%28x%29sqrt%28x-5%29=12
sqrt%28x%29sqrt%28x-5%29=6
Square both sides.
x%28x-5%29=36
x%5E2-5x=36
x%5E2-5x-36=0
Factor.
%28x-9%29%28x%2B4%29=0
Two solutions:
x-9=0
x=9
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x%2B4=0
x=-4
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Go back and verify the solutions.
+x=9
+sqrt%28x%29%2B+sqrt%28x-5%29=sqrt%282x%2B7%29
+sqrt%289%29%2B+sqrt%289-5%29=sqrt%282%289%29%2B7%29
+3%2Bsqrt%284%29=sqrt%2825%29
+3%2B2=5
+5=5
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+x=-4
Not a solution since the square root of a negative number in undefined.