document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=950347>Question 950347</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An interger is four less than twice another. If the product of the two intergers is 70, one pair of intergers that will satisfy the problem is____. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #580295 by </B><A HREF=/tutors/aboutme.mpl?userid=macston><B>macston(5194)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=macston><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=macston><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=580295\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> F=first integer; S= second integer<BR>\n" );
document.write( "FS=70<BR>\n" );
document.write( "S=70/F<BR>\n" );
document.write( "F-4=2S Substitute for S<BR>\n" );
document.write( "F-4=2(70/F)<BR>\n" );
document.write( "F-4=140/F Multiply each side by F.<BR>\n" );
document.write( "F^2-4F=140 Subtract 140 from each side.<BR>\n" );
document.write( "F^2-4F-140=0<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=aF%5E2%2BbF%2Bc=0 ALIGN=MIDDLE  ALT=\"aF%5E2%2BbF%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1F%5E2%2B-4F%2B-140+=+0 ALIGN=MIDDLE  ALT=\"1F%5E2%2B-4F%2B-140+=+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=F%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"F%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=%28-4%29%5E2-4%2A1%2A-140=576 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-4%29%5E2-4%2A1%2A-140=576\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=576 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--4%2B-sqrt%28+576+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--4%2B-sqrt%28+576+%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=F%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+576+%29%29%2F2%5C1+=+14 ALIGN=MIDDLE  ALT=\"F%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+576+%29%29%2F2%5C1+=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F%5B2%5D+=+%28-%28-4%29-sqrt%28+576+%29%29%2F2%5C1+=+-10 ALIGN=MIDDLE  ALT=\"F%5B2%5D+=+%28-%28-4%29-sqrt%28+576+%29%29%2F2%5C1+=+-10\"   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=1F%5E2%2B-4F%2B-140 ALIGN=MIDDLE  ALT=\"1F%5E2%2B-4F%2B-140\"   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=1F%5E2%2B-4F%2B-140+=+1%28F-14%29%2A%28F--10%29 ALIGN=MIDDLE  ALT=\"1F%5E2%2B-4F%2B-140+=+1%28F-14%29%2A%28F--10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 14, -10.\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%2B-4%2Ax%2B-140+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B-140+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "Answers F=14 and F=-10  <BR>\n" );
document.write( "S=70/F=70/14=5 ANSWER 1: One pair of integers that satisfies the problem is 14 and 5.<BR>\n" );
document.write( "For F=-10<BR>\n" );
document.write( "S=70/F=70/-10=-7 ANSWER 2: Another pair of numbers that satisfies the problem is -10 and -7. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );