document.write( "Question 358121: I have to solve and check this equation: sqrt(2x)=-12. I believe it has no solution, but I don't know how to show my work! \n" ); document.write( "

Algebra.Com's Answer #255798 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"sqrt%282x%29=-12\"$
\n" ); document.write( "You are right. A square root cannot be a negative number.

\n" ); document.write( "If this logic is insufficient \"work\", then you could proceed as if you didn't notice this inconsistency:
\n" ); document.write( "Square both sides:
\n" ); document.write( " $\"%28sqrt%282x%29%29%5E2+=+%28-12%29%5E2\"$
\n" ); document.write( "2x = 144
\n" ); document.write( "Divide both sides by 2:
\n" ); document.write( "x = 72

\n" ); document.write( "At this point it appears that we have a solution. But whenever you square both sides of an equation, like we have, you must check your answers. (Squaring both sides of an equation can introduce what a called \"extraneous solutions\". Extraneous solutions are solutions that work in the squared equation but not in the original equation.

\n" ); document.write( "Checking x = 72 in the original equation:
\n" ); document.write( " $\"sqrt%282%2872%29%29=-12\"$
\n" ); document.write( " $\"sqrt%28144%29=-12\"$
\n" ); document.write( " $\"12+=+-12\"$ and the check fails! x = 72 is an extraneous solution and must be rejected. Since we have rejected the only \"solution\", there are no solutions to your equation. \n" ); document.write( "

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