document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=856>Question 856</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please explain to me how you find the answer to this problem: If two parallel sides of a square are increased by 6 cm and the other two parallel sides are each decreased by 1 cm, a rectangle is formed having twice the area of the square. How long was each side of the square? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #292 by </B><A HREF=/tutors/aboutme.mpl?userid=usyim88hk><B>usyim88hk(158)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=usyim88hk><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=292\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the length of one side of the square be x:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+ ALIGN=MIDDLE  ALT=\"+x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the area of the square<BR>\n" );
document.write( "Area of the retangle:<BR>\n" );
document.write( "(x+6)(x-1)<BR>\n" );
document.write( "which is equal to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2%2B5x-6+ ALIGN=MIDDLE  ALT=\"+x%5E2%2B5x-6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so if the area of the retangle is twice the area of the square, then we can set up an equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2%2B5x-6=2x%5E2+ ALIGN=MIDDLE  ALT=\"+x%5E2%2B5x-6=2x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now, slove it:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2%2B5x-6-x%5E2=2x%5E2-x%5E2+ ALIGN=MIDDLE  ALT=\"+x%5E2%2B5x-6-x%5E2=2x%5E2-x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5x-6=x%5E2+ ALIGN=MIDDLE  ALT=\"+5x-6=x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5x-6-x%5E2=x%5E2-x%5E2+ ALIGN=MIDDLE  ALT=\"+5x-6-x%5E2=x%5E2-x%5E2+\"   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%2B5x-6=0+ ALIGN=MIDDLE  ALT=\"+-x%5E2%2B5x-6=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now use the quadratic formula to slove:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28%28-5%29+%2B-+sqrt%28%28-5%5E2%29-4%2A%28-1%29%2A%28-6%29%29%2F%282%2A%28-1%29%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28%28-5%29+%2B-+sqrt%28%28-5%5E2%29-4%2A%28-1%29%2A%28-6%29%29%2F%282%2A%28-1%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28%28%28-5%29+%2B-+sqrt%28%2825-24%29%29%29%2F%28-2%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28%28%28-5%29+%2B-+sqrt%28%2825-24%29%29%29%2F%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28%28%28-5%29%2B-+1%29%2F%28-2%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28%28%28-5%29%2B-+1%29%2F%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = (-4/-2) or (-6/-2)<BR>\n" );
document.write( "x = 2 or 3<BR>\n" );
document.write( "-------------------------------------------------------------<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "if x=2<BR>\n" );
document.write( "x^2 = 4<BR>\n" );
document.write( "(2+6)(2-1) = 8<BR>\n" );
document.write( "8 = 2*4<BR>\n" );
document.write( "8=8 (2 is right!)<BR>\n" );
document.write( "if x=3<BR>\n" );
document.write( "x^2 = 9<BR>\n" );
document.write( "(3+6)(3-1) = 18<BR>\n" );
document.write( "18 = 2*9<BR>\n" );
document.write( "18=18 (3 is right!)<BR>\n" );
document.write( "--------------------------------------------------------------<BR>\n" );
document.write( "So the answer is 2 or 3, they both work! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );