SOLUTION: Which is the extraneous solution of -x = √2x+15? The options are -5, -3, 3, or 5. Extraneous solutions are very hard for me to find. Thank you for any help!

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Question 1001292: Which is the extraneous solution of -x = √2x+15?
The options are -5, -3, 3, or 5.
Extraneous solutions are very hard for me to find. Thank you for any help!
Found 2 solutions by KMST, rothauserc:
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Solutions to -x=sqrt%282x%2B15%29 will be some of the solutions to %28-x%29%5E2=%28sqrt%282x%2B15%29%29%5E2 .
We solve the second equation:
x%5E2=2x%2B15
x%5E2-2x=15
x%5E2-2x%2B1=16
%28x-1%29%5E2=16
The solutions are:
x-1=4--->x=5 , and
x-1=-4--->x=-3 .
If one of them is not a solution of the original equation,
that one is an extraneous solution.
Since -x=sqrt%282x%2B15%29 obviously requires a negative x ,
it is easy to see that 5 is an extraneous solution.
You can check and see that
x=-3 is a solution to the original equation.

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
-x = sqrt(2x + 15)
square both sides of =
x^2 = 2x + 15
x^2 -2x -15 = 0
(x-5)*(x+3) = 0
x = 5 or -3
check answers
-(-3) = sqrt(9)
3 = 3
-5 = sqrt(25)
-5 = 5
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-5 is the extraneous root
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here is the graph of both equations, -x is red and sqrt(2x+15) is green
+graph%28+300%2C+200%2C+-10%2C+2%2C+-2%2C+10%2C+-x%2C+sqrt%282x%2B15%29%29+
solution is the intersection of the equations, therefore
x = -3