SOLUTION: Solve x^2 + sqrt 22x = 0

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Question 172238This question is from textbook Introductory Algebra
: Solve
x^2 + sqrt 22x = 0
This question is from textbook Introductory Algebra

Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
Solve


Isolate the radical term by subtracting  from both sides:



Square both sides:











We must always check even-root radical equations,
because there may be extraneous solutions,

Checking 






root(3,22)
Checking 












That is false so  is not a
solution.

So  is the only solution.

-------------------

Here is how we could have solved this much easier:



Isolate the radical term by subtracting  from both sides:



A square root radical always represents a non-negative number,
so the left side is non-negative.  The right side, however, will
always be negative unless .  So 0 is the only possible
solution, and we check it as above and find it is a solution,
so the only solution is .

Edwin



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