document.write( "Question 812219: how would you solve 16h to the 5th minus 25 h to the 3rd plus 9h equals 0 \n" ); document.write( "

Algebra.Com's Answer #489056 by KMST(5328) $\"\"$ $\"About$

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$\"16h%5E5-25h%5E3%2B9h=0\"$
\n" ); document.write( " $\"%2816h%5E4-25h%5E2%2B9%29h=0\"$ --> $\"highlight%28x=0%29\"$ is one solution
\n" ); document.write( "The other solutions, if there are any, must come from
\n" ); document.write( " $\"16h%5E4-25h%5E2%2B9=0\"$
\n" ); document.write( "I know that I can factor $\"16y%5E2-25y%2B9=%2816y-9%29%28y-1%29\"$ , so
\n" ); document.write( " $\"16h%5E4-25h%5E2%2B9=%2816h%5E2-9%29%28h%5E2-1%29\"$
\n" ); document.write( "and that can be applied to transform the equation:
\n" ); document.write( " $\"16h%5E4-25h%5E2%2B9=0\"$
\n" ); document.write( " $\"%2816h%5E2-9%29%28h%5E2-1%29=0\"$
\n" ); document.write( " $\"%284h%2B3%29%284h-3%29%28h%2B1%29%28h-1%29=0\"$
\n" ); document.write( "So, the other solutions are
\n" ); document.write( " $\"highlight%28h=-3%2F4%29\"$ , $\"highlight%28h=3%2F4%29\"$ ,
\n" ); document.write( " $\"highlight%28h=-1%29\"$ , and $\"highlight%28h=1%29\"$ .
\n" ); document.write( "
\n" ); document.write( "NOTE: You could also say that from $\"16h%5E4-25h%5E2%2B9=0\"$ ,
\n" ); document.write( "we do the change of variable $\"y=h%5E2\"$
\n" ); document.write( "to get the quadratic equation $\"16y%5E2-25y%2B9=0\"$ ,
\n" ); document.write( "with solutions $\"y=1\"$ and $\"y=9%2F16\"$
\n" ); document.write( "and returning from $\"y\"$ to $\"h\"$ we get
\n" ); document.write( " $\"h%5E2=1\"$ --> $\"system%28h=1%2C+%22or%22+%2Ch=-1%29\"$
\n" ); document.write( "and
\n" ); document.write( " $\"h%5E2=9%2F16\"$ --> $\"system%28h=3%2F4%2C+%22or%22+%2Ch=-3%2F4%29\"$ . \n" ); document.write( "

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