SOLUTION: I am having a problem solving this problem: For the equation x - the square root of x = 0 , perform the following: Solve for all values of x that satisfies the equation Thanks

Question 51900: I am having a problem solving this problem:
For the equation x - the square root of x = 0 , perform the following:
Solve for all values of x that satisfies the equation
Thanks for your help.
Answer by funmath(2933) (Show Source): You can put this solution on YOUR website!
This one can be solved a couple of different ways. One way is to factor out the sqrt of x:
x-sqrt(x)=0
sqrt(x)(sqrt(x)-1)=0
Use the zero product property and set sqrt(x)=0 and sqrt(x)-1=0 and solve for x.
sqrt(x)=0
(sqrt(x))^2=(0)^2 square both sides
x=0 simplify
and
sqrt(x)-1=0
sqrt(x)-1+1=0+1 add 1 to both sides
sqrt(x)=1 simplify
(sqrt(x))^2=(1)^2 square both sides
x=1 simplify
When you are dealing with square roots, you must check for false solutions called extraneous solutions. We do this by substituting the answers we get back into the original equation and making sure that both sides of the equation equal each other.
Our solutions were x=0 and x=1
(0)-sqrt(0)=0 substitute 0 into original equation
0-0=0 This proves x=0 is a good solution.
(1)-sqrt(1)=0 substitute 1 into the original equation
1-1=0 This proves x=1 is a good solution.
Therefore, your solution is x=0 and x=1

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