document.write( "Question 171916: Solve by completing the square
\n" ); document.write( "3x^2+5x-1=0 \n" ); document.write( "

Algebra.Com's Answer #127020 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
First add $\"1\"$ to both sides
\n" ); document.write( " $\"3x%5E2+%2B+5x+=+1\"$
\n" ); document.write( "Now divide both sides by $\"3\"$
\n" ); document.write( " $\"x%5E2+%2B+%285%2F3%29%2Ax+=+1%2F3\"$
\n" ); document.write( "Take 1/2 of the coefficient of $\"x\"$ , square it
\n" ); document.write( "and add it to both sides
\n" ); document.write( " $\"x%5E2+%2B+%285%2F3%29%2Ax+%2B+%285%2F6%29%5E2+=+%285%2F6%29%5E2+%2B+1%2F3\"$
\n" ); document.write( "The thing to realize at this point is that the
\n" ); document.write( "left side is a perfect square. It is
\n" ); document.write( " $\"%28x+%2B+5%2F6%29%5E2\"$ , so
\n" ); document.write( " $\"%28x+%2B+5%2F6%29%5E2+=+25%2F36+%2B+12%2F36\"$
\n" ); document.write( " $\"%28x+%2B+5%2F6%29%5E2+=+37%2F36\"$
\n" ); document.write( "Take the square root of both sides
\n" ); document.write( " $\"x+%2B+5%2F6+=+sqrt%2837%29%2F6\"$
\n" ); document.write( "Solve for $\"x\"$
\n" ); document.write( " $\"x+=+%28sqrt%2837%29+-+5%29+%2F+6\"$
\n" ); document.write( "and
\n" ); document.write( " $\"x+=+%28-sqrt%2837%29+-+5%29+%2F+6\"$
\n" ); document.write( "Both answers are correct \n" ); document.write( "

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