SOLUTION: {{{x=sqrt(x-1)+3}}}

Question 742096:
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
We can isolate the square root on one side of the equal sign.
After that we can square both sides of the equal sign to get an equation without a square root.
The new equation will have the same solutions as the original equation, and could have some extra solutions, that we call "extraneous solutions".
We do not worry about extraneous solutions at the beginning, because we will check all solutions. We will check to see if they are really solutions to the original equation. We can eliminate any and all extraneous solutions with that checking step.

FINDING POSSIBLE SOLUTIONS:
--> --> --> --> -->
Factoring,
-->
(You could also solve by applying the quadratic formula or by completing the square, if you do not like factoring)
Any way we solve that quadratic equation, we get the tentative solutions or
They are solutions of ,
but are they solutions of ?

CHECKING:
For , shows that is not a solution of .
It is an extraneous solution.

The value results in , which makes true.
That means that is truly a solution of . It is the solution to .
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