document.write( "Question 412980: I meant I need help completing the square
\n" ); document.write( "6x^2+5x=6 \n" ); document.write( "

Algebra.Com's Answer #289954 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
I can help
\n" ); document.write( " $\"6x%5E2+%2B+5x+=+6\"$
\n" ); document.write( "first, divide through by $\"6\"$ , so
\n" ); document.write( " $\"x%5E2\"$ has coefficient = $\"1\"$
\n" ); document.write( " $\"x%5E2+%2B+%285%2F6%29%2Ax+=+1\"$
\n" ); document.write( "Now take 1/2 of the coefficient of $\"x\"$ ,
\n" ); document.write( "square it, and add it to both sides
\n" ); document.write( " $\"+x%5E2+%2B+%285%2F6%29%2Ax+%2B+%285%2F12%29%5E2+=+1++%2B++%285%2F12%29%5E2\"$
\n" ); document.write( " $\"x%5E2+%2B++%285%2F6%29%2Ax+%2B+25%2F144+=+144%2F144+%2B+25%2F144\"$
\n" ); document.write( " $\"+x%5E2+%2B++%285%2F6%29%2Ax+%2B+25%2F144+=+169%2F144+\"$
\n" ); document.write( "Both sides are now a perfect square
\n" ); document.write( " $\"+%28x+%2B+5%2F12%29%5E2+=+%2813%2F12%29%5E2\"$
\n" ); document.write( "Take the square root of both sides
\n" ); document.write( " $\"x+%2B+5%2F12+=+13%2F12\"$
\n" ); document.write( " $\"x+=+8%2F12\"$
\n" ); document.write( " $\"x+=+2%2F3\"$
\n" ); document.write( "And there is also a negative square root
\n" ); document.write( " $\"x+%2B+5%2F12+=+-13%2F12\"$
\n" ); document.write( " $\"x+=+-3%2F2\"$
\n" ); document.write( "The roots are 2/3 and -3/2
\n" ); document.write( "I can check this by
\n" ); document.write( " $\"%28x+-+2%2F3%29%2A%28x+%2B+3%2F2%29+=+0\"$
\n" ); document.write( " $\"x%5E2+-%28+2%2F3%29%2Ax+%2B+%283%2F2%29%2Ax+-+1+=+0\"$
\n" ); document.write( " $\"x%5E2+-%284%2F6%29%2Ax+%2B+%289%2F6%29%2Ax+=+1\"$
\n" ); document.write( "Multiply through by $\"6\"$
\n" ); document.write( " $\"6x%5E2+-+4x+%2B+9x+=+6\"$
\n" ); document.write( " $\"6x%5E2+%2B+5x+=+6\"$
\n" ); document.write( "OK\r
\n" ); document.write( "
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