document.write( "Question 189450This question is from textbook
\n" ); document.write( ": In solving the question x^2 =x, a student cancels the x on both sides, giving x=1. Comment on the validity of such manipulation. How do we correct such action if it is wrong. \n" ); document.write( "

Algebra.Com's Answer #142112 by Earlsdon(6294) $\"\"$ $\"About$

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$\"x%5E2+=+x\"$ While canceling (dividing by) an x on both sides seems to be a valid mathematical operation, it ignores the fact that the equation is, in fact, a quadratic equation and will have two solutions (roots or zeros).
\n" ); document.write( "The correct procedure is to subtract x from both sides giving you...
\n" ); document.write( " $\"x%5E2+-+x+=+0\"$ The factor an x from the left side:
\n" ); document.write( " $\"x%2A%28x-1%29+=+0\"$ Now apply the zero product rule:
\n" ); document.write( " $\"+x+=+0+\"$ or $\"x-1+=+0\"$ so the two solutions are:
\n" ); document.write( " $\"+x+=+0+\"$ and $\"x+=+1\"$ \n" ); document.write( "

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