document.write( "Question 120103: How would I solve this quadratic equation?:\r
\n" ); document.write( "\n" ); document.write( " $\"y%5E3-28y%5E1.5%2B27=0\"$ \r
\n" ); document.write( "\n" ); document.write( "(I used decimal exponents because i have no idea how to write fractional exponents on a computer)\r
\n" ); document.write( "\n" ); document.write( "I have a very rough idea of where to start but am still having a lot of trouble, please help!\r
\n" ); document.write( "\n" ); document.write( "James\r
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Algebra.Com's Answer #88035 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Solve for y:
\n" ); document.write( " $\"y%5E3-28y%5E%281.5%29%2B27+=+0\"$
\n" ); document.write( "You can solve this problem by substituting another varible for y as follows:
\n" ); document.write( "Let $\"z+=+y%5E%281.5%29\"$ , then $\"z%5E2+=+y%5E3\"$
\n" ); document.write( " $\"z%5E2-28z%2B27+=+0\"$ Now you can solve this quadratic equation by factoring:
\n" ); document.write( " $\"%28z-1%29%28z-27%29+=+0\"$ Apply the zero product principle:
\n" ); document.write( " $\"z-1+=+0\"$ or $\"z-27+=+0\"$
\n" ); document.write( "If $\"z-1+=+0\"$ then $\"z+=+1\"$
\n" ); document.write( "If $\"z-27+=+0\"$ then $\"z=27\"$
\n" ); document.write( "But we said that $\"z+=+y%5E1.5\"$ , so we make the substitution back:
\n" ); document.write( " $\"y%5E1.5+=+1\"$ or $\"y%5E1.5+=+27\"$
\n" ); document.write( "Let's rewrite the exponents:
\n" ); document.write( " $\"y%5E1.5+=+y%5E%283%2F2%29\"$
\n" ); document.write( " $\"y%5E%283%2F2%29+=+1\"$ which can also be written:
\n" ); document.write( " $\"%28sqrt%28y%29%29%5E3+=+1\"$ Take the cube-root of both sides.
\n" ); document.write( " $\"sqrt%28y%29+=+1\"$ Now square both sides.
\n" ); document.write( " $\"y+=+1\"$ and...
\n" ); document.write( " $\"y%5E%283%2F2%29+=+27\"$
\n" ); document.write( " $\"%28sqrt%28y%29%29%5E3+=+27\"$ Take the cube-root of both sides.
\n" ); document.write( " $\"sqrt%28y%29+=+3\"$ Now square both sides.
\n" ); document.write( " $\"y+=+9\"$
\n" ); document.write( "The solutions are:
\n" ); document.write( " $\"y+=+1\"$ , $\"y+=+9\"$ \n" ); document.write( "

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