document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=34925>Question 34925</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have to solve each problem then check my answer to be sure it is reasonable. Here's the problem:<BR>\n" );
document.write( "  A ten-gallon aquarium holding African cichlids is 3 inches higher than it is wide. It's length is 21 inches, and its volume is 2730 cubic inches. What are the height and width of the aquarium?\r<BR>\n" );
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document.write( "I have set it up to look like this:<BR>\n" );
document.write( " (x-7)~2 + (x+1)~2 + x~2 then I have gotten that figured out to x~2-14x+49+x~2+2x+1=x~2  that is where I get stuck after subtracting the x~2 to get it on the same side as the rest of the equation.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #21171 by </B><A HREF=/tutors/aboutme.mpl?userid=mbarugel><B>mbarugel(146)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mbarugel><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=21171\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hello!<BR>\n" );
document.write( "Let's call X to the width of the aquarium. We know that its height must be X+3. Also, its length is 21. Volume is calculated as width*height*length. So we get the following equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%28X%2B3%2921+=+2730 ALIGN=MIDDLE  ALT=\"X%28X%2B3%2921+=+2730\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%28X%2B3%29+=+2730%2F21+=+130 ALIGN=MIDDLE  ALT=\"X%28X%2B3%29+=+2730%2F21+=+130\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%5E2+%2B+3X+=+130 ALIGN=MIDDLE  ALT=\"X%5E2+%2B+3X+=+130\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%5E2+%2B+3X+-+130+=+0 ALIGN=MIDDLE  ALT=\"X%5E2+%2B+3X+-+130+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we can solve this quadratic equation using the standard procedure:\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B3x%2B-130+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B3x%2B-130+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%283%29%5E2-4%2A1%2A-130=529 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%283%29%5E2-4%2A1%2A-130=529\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=529 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-3%2B-sqrt%28+529+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-3%2B-sqrt%28+529+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%283%29%2Bsqrt%28+529+%29%29%2F2%5C1+=+10 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%283%29%2Bsqrt%28+529+%29%29%2F2%5C1+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%283%29-sqrt%28+529+%29%29%2F2%5C1+=+-13 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%283%29-sqrt%28+529+%29%29%2F2%5C1+=+-13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B3x%2B-130 ALIGN=MIDDLE  ALT=\"1x%5E2%2B3x%2B-130\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B3x%2B-130+=+%28x-10%29%2A%28x--13%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B3x%2B-130+=+%28x-10%29%2A%28x--13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 10, -13.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-130+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-130+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "As you can see the two solution are 10 and -13. We can disregard the -13 because width can't be negative. So we conclude that the width of the aquarium is 10 inches. Therefore, its height must be 13 inches.\r<BR>\n" );
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document.write( "You can check that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2A13%2A21+=+2730 ALIGN=MIDDLE  ALT=\"10%2A13%2A21+=+2730\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I hope this helps!<BR>\n" );
document.write( "Get more answers at <a  rel=nofollow HREF=http://www.onlinemathanswers.com>Online Math Answers.com</a>!<BR>\n" );
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