document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=159823>Question 159823</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780618803712/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A square piece of cardboard is formed into a box by cutting out 2-inch squares from each of the corners and folding up the sides. If the volume of the box needs to be 84.5 cubic inches, what size square piece of cardboard is needed? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #117858 by </B><A HREF=/tutors/aboutme.mpl?userid=checkley77><B>checkley77(12844)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=checkley77><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=117858\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=the sides of the square piece of cardboard.<BR>\n" );
document.write( "Cutting a 2 in. square out of each corner leaves the base measurements:<BR>\n" );
document.write( "(x-4)^2=x^2-8x+16<BR>\n" );
document.write( "The height is 2 in.<BR>\n" );
document.write( "volume=2(x^2-8x+16)<BR>\n" );
document.write( "84.5=2x^2-16x+32<BR>\n" );
document.write( "2x^2-16x+32-84.5=0<BR>\n" );
document.write( "2x^2-16x-52.5=0<BR>\n" );
document.write( "(x-10.5)(x+2.5)=0<BR>\n" );
document.write( "x-10.5=0<BR>\n" );
document.write( "x=10.5 inches is the original side of the piece of square cardboard.<BR>\n" );
document.write( "Proof:<BR>\n" );
document.write( "84.5=2(10.5^2-8*10.5+16)<BR>\n" );
document.write( "84.5=2(110.25-84+16)<BR>\n" );
document.write( "84.5=2*42.25<BR>\n" );
document.write( "84.5=84.5<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );