document.write( "Question 331424: solve the quadratic equation by using the COMPLETING THE SQUARE method and applying the square root property.\r
\n" ); document.write( "\n" ); document.write( " $\"n%5E2-2%2F3n=1%2F9\"$
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Algebra.Com's Answer #237668 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

You can put this solution on YOUR website!
Solve the quadratic equation by using the COMPLETING THE SQUARE method and
\n" ); document.write( "applying the square root property.
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\n" ); document.write( "I think the problem should be:
\n" ); document.write( " $\"n%5E2-%282%2F3%29n+=+1%2F9\"$
\n" ); document.write( ":
\n" ); document.write( " $\"n%5E2-%282%2F3%29n+%2B+____+=+1%2F9\"$
\n" ); document.write( ":
\n" ); document.write( " $\"%281%2F3%29%5E2\"$ = $\"1%2F9\"$ completes the square
\n" ); document.write( " $\"n%5E2-%282%2F3%29n+%2B+1%2F9\"$ = $\"1%2F9+%2B+1%2F9\"$
\n" ); document.write( " $\"n%5E2-%282%2F3%29n+%2B+1%2F9\"$ = $\"2%2F9\"$
\n" ); document.write( " $\"%28n-1%2F3%29%5E2\"$ = $\"2%2F9\"$
\n" ); document.write( "Find the square root of both sides
\n" ); document.write( " $\"n-1%2F3\"$ = +/- $\"sqrt%282%2F9%29\"$
\n" ); document.write( "Extract 1/3 from 1/9
\n" ); document.write( " $\"n-1%2F3\"$ = +/- $\"sqrt%282%29%2F3\"$
\n" ); document.write( "n = $\"1%2F3\"$ +/- $\"sqrt%282%29%2F3\"$
\n" ); document.write( "Two solutions
\n" ); document.write( "n = $\"%281+%2B+sqrt%282%29%29%2F3\"$
\n" ); document.write( "and
\n" ); document.write( "n = $\"%281+-+sqrt%282%29%29%2F3\"$
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\n" ); document.write( "One way to check this problem:
\n" ); document.write( "Use a cal, find that the approx decimal value for $\"%281+%2B+sqrt%282%29%29%2F3\"$ = .8047
\n" ); document.write( "Substitute this value for n in the original problem find the value
\n" ); document.write( ".8047^2 - $\"2%2F3\"$ (.8047) = .111 which is the decimal value of 1/9, ,1111
\n" ); document.write( "confirms our solution, you can do the same with $\"%281+-+sqrt%282%29%29%2F3\"$ \n" ); document.write( "

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