document.write( "Question 34498: x^2+x+5=0 \n" ); document.write( "

Algebra.Com's Answer #20770 by lyra(94) $\"\"$ $\"About$

You can put this solution on YOUR website!
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ (in our case $\"1x%5E2%2B1x%2B5+=+0\"$ ) has the following solutons:
\n" ); document.write( "
\n" ); document.write( " $\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"$
\n" ); document.write( "
\n" ); document.write( " For these solutions to exist, the discriminant $\"b%5E2-4ac\"$ should not be a negative number.
\n" ); document.write( "
\n" ); document.write( " First, we need to compute the discriminant $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%281%29%5E2-4%2A1%2A5=-19\"$ .
\n" ); document.write( "
\n" ); document.write( " The discriminant -19 is less than zero. That means that there are no solutions among real numbers.

\n" ); document.write( " If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

\n" ); document.write( "
\n" ); document.write( " In the field of imaginary numbers, the square root of -19 is + or - $\"sqrt%28+19%29+=+4.35889894354067\"$ .
\n" ); document.write( "
\n" ); document.write( " The solution is

\n" ); document.write( "
\n" ); document.write( " Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B5+%29\"$

\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Hope this helps,
\n" ); document.write( "lyra \n" ); document.write( "

\n" );