SOLUTION: solve. x= (x-2)squareroot x im not good at square roots!!

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Question 199251: solve. x= (x-2)squareroot x

im not good at square roots!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x=%28x-2%29%2Asqrt%28x%29 Start with the given equation.


x%5E2=%28x-2%29%5E2%2Ax Square both sides.


x%5E2=x%28x-2%29%5E2 Rearrange the terms.


x%5E2=x%28x%5E2-4x%2B4%29 FOIL


x%5E2=x%5E3-4x%5E2%2B4x Distribute


0=x%5E3-4x%5E2%2B4x-x%5E2 Subtract x%5E2 from both sides.


0=x%5E3-5x%5E2%2B4x Combine like terms.


0=x%28x%5E2-5x%2B4%29 Factor out the GCF "x"


0=x%28x-1%29%28x-4%29 Factor


x=0 or x-1=0 or x-4=0 Set each factor equal to zero


x=0 or x=1 or x=4 Solve for "x" in each equation.


So the possible solutions are x=0 or x=1 or x=4


However, if you plug in x=1, you'll get a contradiction. So x=1 is NOT a solution.


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Answer:

So the solutions are x=0 or x=4