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!

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) (Show Source): You can put this solution on YOUR website!
Solutions to will be some of the solutions to .
We solve the second equation:

The solutions are:
---> , and
---> .
If one of them is not a solution of the original equation,
that one is an extraneous solution.
Since obviously requires a negative ,
it is easy to see that 5 is an extraneous solution.
You can check and see that
is a solution to the original equation.
Answer by rothauserc(4718) (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

solution is the intersection of the equations, therefore
x = -3

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SOLUTION: Which is the extraneous solution of -x = &#8730;2x+15? The options are -5, -3, 3, or 5. Extraneous solutions are very hard for me to find. Thank you for any help!

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!