document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=365065>Question 365065</A>: <I><SPAN STYLE=\"word-break: break-all;\"> squares are cut from  the corners of a rectangle sheet of metal 30 in by 50 in. the four sides are then turned up and soldered. how large are the squares if the volume of the resulting open metal box is 2,392 cubic inches? 4,000 cubic inches? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #260439 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=260439\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> squares are cut from the corners of a rectangle sheet of metal 30 in by 50 in.<BR>\n" );
document.write( " the four sides are then turned up and soldered.<BR>\n" );
document.write( " how large are the squares if the volume of the resulting open metal box is<BR>\n" );
document.write( " 2,392 cubic inches?<BR>\n" );
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document.write( "Let x = length of the side of the 4 squares removed<BR>\n" );
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document.write( "Then the dimensions of the open box will be:<BR>\n" );
document.write( "L = 50-2x<BR>\n" );
document.write( "W = 30-2x<BR>\n" );
document.write( "H = x<BR>\n" );
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document.write( "Volume of the box; L*W*H:<BR>\n" );
document.write( "(50-2x)*(30-2x)*x = 2392 cu/in<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "(1500 - 100x - 60x + 4x^2)*x = 2392<BR>\n" );
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document.write( "x(4x^2 - 160x + 1500) = 2392<BR>\n" );
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document.write( "4x^3 - 160x^2 + 1500x - 2392 = 0<BR>\n" );
document.write( "Simplify, divide by 4<BR>\n" );
document.write( "x^3 - 40x^2 + 375x - 598 = 0<BR>\n" );
document.write( "Plot this equation (Red)<BR>\n" );
document.write( "x = 2 inches is the reasonable solution<BR>\n" );
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document.write( "4000 cu inches<BR>\n" );
document.write( "x^3 - 40x^2 + 375x - 1000<BR>\n" );
document.write( "plot this equation also (green)<BR>\n" );
document.write( "x = 5 inches, but we have two reasonable solutions<BR>\n" );
document.write( "or<BR>\n" );
document.write( "x = 7 inches\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );