document.write( "Question 829204: Hi, the equation is: X - 4*(square root X) = 32. I thought about squaring both sides to get a quadratic, but that would still leave a (square root of x) in the equation. Thanks for any help you can provide. \n" ); document.write( "

Algebra.Com's Answer #499749 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
If there is only one square root, you want to isolate it on one side of the equation before squaring.
\n" ); document.write( " $\"x-4sqrt%28x%29=32\"$
\n" ); document.write( " $\"-4sqrt%28x%29=32-x\"$ or $\"x-32=4sqrt%28x%29\"$
\n" ); document.write( "Also, if $\"sqrt%28x%29\"$ has to be a real number, it must be that $\"x%3E=0\"$ .
\n" ); document.write( "Now we can square both sides, knowing that we may be introducing some exraneous solutions.
\n" ); document.write( " $\"%28x-32%29%5E2=%284sqrt%28x%29%29%5E2\"$
\n" ); document.write( " $\"x%5E2-64x%2B1024=4%5E2%2A%28sqrt%28x%29%29%5E2\"$
\n" ); document.write( " $\"x%5E2-64x%2B1024=16x\"$
\n" ); document.write( " $\"x%5E2-64x%2B1024-16x=0\"$
\n" ); document.write( " $\"x%5E2-80x%2B1024=0\"$
\n" ); document.write( "Factoring, since $\"x%5E2-80x%2B1024=%28x-16%29%28x-64%29\"$ , we transform the equation into
\n" ); document.write( " $\"%28x-16%29%28x-64%29=0\"$ , whose solutions are
\n" ); document.write( " $\"x=16\"$ and $\"x=64\"$
\n" ); document.write( "Is any one of those an extraneous solution?
\n" ); document.write( "For $\"x=16\"$ ,
\n" ); document.write( " $\"x-4sqrt%28x%29=16-4sqrt%2816%29=16-4%2A4=16-16=0\"$ so $\"x=16\"$ is not a solution of the original equation. It's an extraneous solution, introduced when we squared both sides.
\n" ); document.write( "For $\"x=64\"$ ,
\n" ); document.write( " $\"x-4sqrt%28x%29=64-4sqrt%2864%29=64-4%2A8=64-32=32\"$ So $\"highlight%28x=64%29\"$ is a solution to the original equation. \n" ); document.write( "

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