document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=901966>Question 901966</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a framed picture has lenght 35 cm and width 25 cm. the picture itself has area 375 cm. how far is it from the edge of the picture of the frame if its distance is uniform around the picture </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #547026 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=547026\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a framed picture has lenght 35 cm and width 25 cm. the picture itself has area 375 cm. how far is it from the edge of the picture of the frame if its distance is uniform around the picture<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Let x = width (cm) of frame<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(35-2x)(25-2x) =375<BR>\n" );
document.write( "875 - 70x - 50x + 4x^2 = 375<BR>\n" );
document.write( "875 - 120x + 4x^2 = 375<BR>\n" );
document.write( "4x^2 - 120x + 875 = 375<BR>\n" );
document.write( "4x^2 - 120x + 575 = 0<BR>\n" );
document.write( ".<BR>\n" );
document.write( "applying the quadratic formula we get:<BR>\n" );
document.write( "x = {24, 6}<BR>\n" );
document.write( "throw out the 24 (extraneous) leaving<BR>\n" );
document.write( "x = 6 cm<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Details of quadratic follows:<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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=quadratic.solver>SOLVE quadratic equation with variable</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=4x%5E2%2B-120x%2B575+=+0 ALIGN=MIDDLE  ALT=\"4x%5E2%2B-120x%2B575+=+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=%28-120%29%5E2-4%2A4%2A575=5200 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-120%29%5E2-4%2A4%2A575=5200\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=5200 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--120%2B-sqrt%28+5200+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--120%2B-sqrt%28+5200+%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-%28-120%29%2Bsqrt%28+5200+%29%29%2F2%5C4+=+24.01387818866 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-120%29%2Bsqrt%28+5200+%29%29%2F2%5C4+=+24.01387818866\"   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-%28-120%29-sqrt%28+5200+%29%29%2F2%5C4+=+5.98612181134003 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-120%29-sqrt%28+5200+%29%29%2F2%5C4+=+5.98612181134003\"   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=4x%5E2%2B-120x%2B575 ALIGN=MIDDLE  ALT=\"4x%5E2%2B-120x%2B575\"   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=4x%5E2%2B-120x%2B575+=+4%28x-24.01387818866%29%2A%28x-5.98612181134003%29 ALIGN=MIDDLE  ALT=\"4x%5E2%2B-120x%2B575+=+4%28x-24.01387818866%29%2A%28x-5.98612181134003%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 24.01387818866, 5.98612181134003.\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+4%2Ax%5E2%2B-120%2Ax%2B575+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-120%2Ax%2B575+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );