Question 268365
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i need help finding x in the equation: 2(squareroot x) + 3 = x
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        In the post by @mananth, the solution is incomplete and is written inaccurately; 

        the answer absents, and from his post, a reader can make wrong conclusion.


        So, I came to present an accurate and complete solution.



2sqrtx +3=x
2sqrtx=x-3
square both the sides of the equation
4x=(x-3)^2
4x=x^2-6x+9
x^2-4x-6x+9=0
x^2-10x+9=0
x^2-9x-x+9=0
x(x-9)-1(x-9)=0
(x-1)(x-9)=0


The roots to the last equation are x= 1  and  x= 9.


The check shows that x= 9 satisfies the original equation,
while x= 1 is an extraneous solution and should be rejected.


<U>ANSWER</U>.  The given equation has a unique solution x = 9.


Solved completely and accurately (as it should be done).