document.write( "Question 26435: w^2-18w+81 =0 \n" ); document.write( "

Algebra.Com's Answer #14279 by Alwayscheerful(414) $\"\"$ $\"About$

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 $\"aw%5E2%2Bbw%2Bc=0\"$ (in our case $\"1w%5E2%2B-18w%2B81+=+0\"$ ) has the following solutons:
\n" ); document.write( "
\n" ); document.write( " $\"w%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"$
\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 $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%28-18%29%5E2-4%2A1%2A81=0\"$ .
\n" ); document.write( "
\n" ); document.write( " Discriminant d=0 is zero! That means that there is only one solution: $\"w+=+%28-%28-18%29%29%2F2%5C1\"$ .
\n" ); document.write( " Expression can be factored: $\"1w%5E2%2B-18w%2B81+=+1%28w-9%29%2A%28w-9%29\"$
\n" ); document.write( "
\n" ); document.write( " Again, the answer is: 9, 9.\n" ); document.write( "Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-18%2Ax%2B81+%29\"$

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

\n" );