document.write( "Question 1163336: factor this quadratic equation\r
\n" ); document.write( "\n" ); document.write( "30(p^2-1)=11p
\n" ); document.write( "

Algebra.Com's Answer #787414 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "    30*(p^2-1) = 11p\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "This equation is EQUIVALENT to this \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \"30p%5E2+-+11p+-+30\" = 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Complete the square, step by step\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \"30p%5E2+-+11p\" = \"30\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \"p%5E2+-+%2811%2F30%29p\" = \"1\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \"p%5E2+-+2%2A%2811%2F60%29p+%2B+%2811%2F60%29%5E2\" = \"1+%2B+%2811%2F60%29%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \"%28p-11%2F60%29%5E2\" = \"1+%2B+121%2F3600\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \"%28p-11%2F60%29%5E2\" = \"3721%2F3600\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \"p+-+11%2F60\" = +/- \"sqrt%283721%2F3600%29\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \"p-11%2F60\" = +/- \"61%2F60\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    p = \"11%2F60\" +/- \"61%2F60\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The roots are  \"p%5B1%5D\" = \"11%2F60+%2B+61%2F60\" = \"72%2F60\" = \"6%2F5\"  and\r\n" );
document.write( "\r\n" );
document.write( "               \"p%5B2%5D\" = \"11%2F60+-+61%2F60\" = - \"50%2F60\" = - \"5%2F6\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hence, the polynomial  \"30p%5E2+-+11p+-+30\"  can be factored in this way\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \"30p%5E2+-+11p+-+30\" = \"30%2A%28p-p%5B1%5D%29%2A%28p-p%5B2%5D%29\" = \"30%2A%28p-6%2F5%29%2A%28p%2B5%2F6%29\" = \"%285p-6%29%2A%286p%2B5%29\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is the factorization the problem wants from you.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );