SOLUTION: Solve: sqrt (2+x) = x

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Question 92162: Solve:
sqrt (2+x) = x
Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%282%2Bx%29=x
Square both sides of the equation:
x%2B2=x%5E2
Put the equation in standard form:
x%5E2-x-2=0
Factor:
%28x-2%29%28x%2B1%29=0
Equate each factor to 0 and solve for x:
x-2=0
x=2
x%2B1=0
x=-1
Now, you need to plug these results back into the original equation to see if it still holds true. You can see that x=2 is a valid answer, since the equation holds when you plug that one in. However, x=-1 does not hold true. That is called an "extraneous root." It's a result of solving the problem, but it is not a valid answer. The only correct answer is:
highlight%28x=2%29
Good Luck,
tutor_paul@yahoo.com