document.write( "Question 175025:
\n" ); document.write( "Find the missing root and solve for k: 2x^2 - 12x + k = 0; r1 = 3 + square root of 2 \n" ); document.write( "

Algebra.Com's Answer #130141 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+2x%5E2+-+12x+%2B+k+=+0\"$
\n" ); document.write( " $\"x%5E2+-+6x+%2B+k%2F2+=+0\"$
\n" ); document.write( "given:
\n" ); document.write( " $\"r%5B1%5D+=+3+%2B+sqrt%282%29\"$
\n" ); document.write( " $\"%28x+-+r%5B1%5D%29%28x+-+r%5B2%5D%29+=+0\"$
\n" ); document.write( " $\"x%5E2+-+%28r%5B1%5D+%2B+r%5B2%5D%29%2Ax+%2B+r%5B1%5Dr%5B2%5D+=+0\"$
\n" ); document.write( " $\"-6+=+-%283+%2B+sqrt%282%29+%2B+r%5B2%5D%29\"$
\n" ); document.write( " $\"r%5B2%5D+=+3+-+sqrt%282%29\"$ the missing root
\n" ); document.write( "------------------------
\n" ); document.write( " $\"k%2F2+=+r%5B1%5Dr%5B2%5D\"$
\n" ); document.write( " $\"k+=+2%2A%283+%2B+sqrt%282%29%29%2Ar%5B2%5D\"$
\n" ); document.write( " $\"k+=+2%2A%283+%2B+sqrt%282%29%29%283+-+sqrt%282%29%29\"$
\n" ); document.write( " $\"k+=+2%2A%289+-+2%29\"$
\n" ); document.write( " $\"k+=+14\"$
\n" ); document.write( "The equation is
\n" ); document.write( " $\"+2x%5E2+-+12x+%2B+14+=+0\"$
\n" ); document.write( "check:
\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"a+=+2\"$
\n" ); document.write( " $\"b+=+-12\"$
\n" ); document.write( " $\"c+=+14\"$
\n" ); document.write( " $\"x+=+%28-%28-12%29+%2B-+sqrt%28+%28-12%29%5E2-4%2A2%2A14+%29%29%2F%282%2A2%29+\"$
\n" ); document.write( " $\"x+=+%28+12+%2B-+sqrt%28+144+-+112+%29%29%2F4+\"$
\n" ); document.write( " $\"x+=+%28+12+%2B-+sqrt%28+32+%29%29%2F4+\"$
\n" ); document.write( " $\"x+=+%283+%2B+sqrt%282%29%29\"$
\n" ); document.write( " $\"x+=+%283+-+sqrt%282%29%29\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

\n" );