document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=575668>Question 575668</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 52. A rectangular painting has dimensions x and x + 10. The painting is in a<BR>\n" );
document.write( "frame 2 in. wide. The total area of the picture and the frame is 900 in.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #369583 by </B><A HREF=/tutors/aboutme.mpl?userid=JBarnum><B>JBarnum(2146)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=JBarnum><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=JBarnum><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=369583\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%28x%2B14%29=900 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%28x%2B14%29=900\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "how did i get this equation?\r<BR>\n" );
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document.write( "the frame is 2 inches thick so theres 2 inches on left side of the length and 2 inches on the right side so thats 4 more inches than the lenth of the picture<BR>\n" );
document.write( "same goes for the width 2 in on top 2 inches on bottom makes 4 more inches added to width<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=LW=A ALIGN=MIDDLE  ALT=\"LW=A\"   DISABLED_style= \"max-width:90%; height:auto;\" > length times width equals area<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=900 ALIGN=MIDDLE  ALT=\"A=900\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=x%2B4 ALIGN=MIDDLE  ALT=\"L=x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=%28x%2B10%29%2B4 ALIGN=MIDDLE  ALT=\"W=%28x%2B10%29%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=x%2B14 ALIGN=MIDDLE  ALT=\"W=x%2B14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "back to the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%28x%2B14%29=900 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%28x%2B14%29=900\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL (First Outer Inner Last)<BR>\n" );
document.write( "F <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Ax=x%5E2 ALIGN=MIDDLE  ALT=\"x%2Ax=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "O <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2A14=14x ALIGN=MIDDLE  ALT=\"x%2A14=14x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ax=4x ALIGN=MIDDLE  ALT=\"4%2Ax=4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "L <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A14=56 ALIGN=MIDDLE  ALT=\"4%2A14=56\"   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%2B14x%2B4x%2B56=900 ALIGN=MIDDLE  ALT=\"x%5E2%2B14x%2B4x%2B56=900\"   DISABLED_style= \"max-width:90%; height:auto;\" > add like terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B18x%2B56=900 ALIGN=MIDDLE  ALT=\"x%5E2%2B18x%2B56=900\"   DISABLED_style= \"max-width:90%; height:auto;\" >subtract 900 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B18x-844=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B18x-844=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > use quadratic formula to solve<BR>\n" );
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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=1x%5E2%2B18x%2B-844+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B18x%2B-844+=+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=%2818%29%5E2-4%2A1%2A-844=3700 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2818%29%5E2-4%2A1%2A-844=3700\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=3700 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+=+%28-18%2B-sqrt%28+3700+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-18%2B-sqrt%28+3700+%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-%2818%29%2Bsqrt%28+3700+%29%29%2F2%5C1+=+21.4138126514911 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2818%29%2Bsqrt%28+3700+%29%29%2F2%5C1+=+21.4138126514911\"   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-%2818%29-sqrt%28+3700+%29%29%2F2%5C1+=+-39.4138126514911 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2818%29-sqrt%28+3700+%29%29%2F2%5C1+=+-39.4138126514911\"   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=1x%5E2%2B18x%2B-844 ALIGN=MIDDLE  ALT=\"1x%5E2%2B18x%2B-844\"   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=1x%5E2%2B18x%2B-844+=+1%28x-21.4138126514911%29%2A%28x--39.4138126514911%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B18x%2B-844+=+1%28x-21.4138126514911%29%2A%28x--39.4138126514911%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 21.4138126514911, -39.4138126514911.\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+1%2Ax%5E2%2B18%2Ax%2B-844+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B18%2Ax%2B-844+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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