document.write( "Question 713018: Can someone please show the steps for this question . please and thanks\r
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\n" ); document.write( "\n" ); document.write( "Use mx^2 + nx+o and write the proof of the quadratic equation using m,n,o
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Algebra.Com's Answer #438285 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!

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document.write( "\"mx%5E2+%2B+nx+%2B+o+=+0\"\r\n" );
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document.write( "\"mx%5E2+%2B+nx+=+-o%0D%0A%0D%0A%7B%7B%7Bexpr%28m%2Fm%29x%5E2+%2B+expr%28n%2Fm%29x+=+-o%2Fm\"\r\n" );
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document.write( "\"x%5E2+%2B+expr%28n%2Fm%29x+=+-o%2Fm\"\r\n" );
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document.write( "Complete the square:\r\n" );
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document.write( "1. Multiply \"expr%28n%2Fm%29\" by \"1%2F2\":\r\n" );
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document.write( "    \"expr%28n%2Fm%29%2Aexpr%281%2F2%29\"\r\n" );
document.write( "    \"n%2F%282m%29\"\r\n" );
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document.write( "2. Square that result:\r\n" );
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document.write( "    \"%28n%2F%282m%29%29%5E2\"\r\n" );
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document.write( "    \"n%5E2%2F%282%5E2m%5E2%29\"\r\n" );
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document.write( "    \"n%5E2%2F%284m%5E2%29\"\r\n" );
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document.write( "3. Add to both sides of \"x%5E2+%2B+expr%28n%2Fm%29x+=+-o%2Fm\"\r\n" );
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document.write( "\"x%5E2+%2B+expr%28n%2Fm%29x+%2B+n%5E2%2F%284m%5E2%29+=+-o%2Fm+%2B+n%5E2%2F%284m%5E2%29\" \r\n" );
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document.write( "Factor the left side;  Get LCD of \"4m%5E2\" on the right\r\n" );
document.write( "and multiply the first term on the right by \"%284m%29%2F%284m%29\"\r\n" );
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document.write( "\"%28x+%2B+n%5E2%2F%282m%29%29%5E2+=+%28-4mo%29%2F%284m%5E2%29+%2B+n%5E2%2F%284m%5E2%29\"\r\n" );
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document.write( "\"%28x+%2B+n%5E2%2F%282m%29%29%5E2+=+%28-4mo%2B+n%5E2%29%2F%284m%5E2%29\"\r\n" );
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document.write( "Use the principle of square roots:\r\n" );
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document.write( "\"x+%2B+n%5E2%2F%282m%29+=++%22%22+%2B-+sqrt%28+%28-4mo%2B+n%5E2%29%2F%284m%5E2%29%29\"\r\n" );
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document.write( "\"x+%2B+n%2F%282m%29+=++%22%22+%2B-+sqrt%28+-4mo%2B+n%5E2%29%2Fsqrt%284m%5E2%29\"\r\n" );
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document.write( " \"x+%2B+n%2F%282m%29+=++%22%22+%2B-+sqrt%28+-4mo%2B+n%5E2%29%2F%282m%29\"\r\n" );
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document.write( "    \"+x+=+-+n%2F%282m%29+%2B-+sqrt%28+-4mo%2B+n%5E2%29%2F%282m%29\"\r\n" );
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document.write( "    \"x+=+%28-n+%2B-+sqrt%28+-4mo%2Bn%5E2+%29%29%2F%282m%29+\" \r\n" );
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document.write( "    \"x+=+%28-n+%2B-+sqrt%28n%5E2-4mo+%29%29%2F%282m%29+\"\r\n" );
document.write( "Edwin
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