document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=231604>Question 231604</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a box with height (x+5) cm has a square base with side x cm. a secong box with height (x+2) cm has a aquare base with side (x+1) cm. if the two boxes have the same volume, find the x value </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #171369 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=171369\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "The volume of a rectangular solid is given by:\r<BR>\n" );
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document.write( "So for your first box:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ V_1\ =\ x\cdot x\cdot(x+5)\ =\ x^3\ +\ 5x^2\">\r<BR>\n" );
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document.write( "And for the second box:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ V_2\ =\ (x+1)(x+1)(x+2)\ =\ x^3\ +\ 4x^2\ +\ 5x\ +\ 2\">\r<BR>\n" );
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document.write( "(verification left as an exercise for the student.)\r<BR>\n" );
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document.write( "Set these two volumes equal to each other:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  \ x^3\ +\ 5x^2\ =\ x^3\ +\ 4x^2\ +\ 5x\ +\ 2\">\r<BR>\n" );
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document.write( "Collect like terms:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 5x\ -\ 2\ =\ 0\">\r<BR>\n" );
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document.write( "Leaving a quadratic that unfortunately does not factor.  Use the quadratic formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x = \frac{-b \pm sqrt{b^2 - 4ac}}{2a} \">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x = \frac{-(-5) \pm sqrt{(-5)^2 - 4(1)(-2)}}{2(1)} \"> \r<BR>\n" );
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document.write( "Of the two roots, one will be negative -- finding them is left as an arithmetic exercise for the student.  Discard the negative root because you are looking for a positive measure of length.  Hint:  Leave your answer in radical form for the exact answer -- at least until you have verified that the root you obtained is the correct answer by using it to calculate the volume of each of the boxes and making sure they are equal quantities -- another exercise for the student.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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