document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=316961>Question 316961</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find three consecutive positive integers such that twice the product of the two smaller integers is 88 more than the product of the two larger integers.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #226887 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=226887\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x,x+2,x+4<BR>\n" );
document.write( "x and x+2 are the 2 smaller numbers<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%28x%2B2%29%29=88%2B%28%28x%2B2%29%28x%2B4%29%29 ALIGN=MIDDLE  ALT=\"2%28x%28x%2B2%29%29=88%2B%28%28x%2B2%29%28x%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \"twice the product of the two smaller integers is 88 more than the product of the two larger integers\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%5E2%2B4x%29=88%2B%28x%5E2%2B6x%2B8%29 ALIGN=MIDDLE  ALT=\"%282x%5E2%2B4x%29=88%2B%28x%5E2%2B6x%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > add<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B4x=x%5E2%2B6x%2B96 ALIGN=MIDDLE  ALT=\"2x%5E2%2B4x=x%5E2%2B6x%2B96\"   DISABLED_style= \"max-width:90%; height:auto;\" > subtract<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x-96=0 ALIGN=MIDDLE  ALT=\"x%5E2-2x-96=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "doesnt come out to a whole number so either thats suppose to be that way in the answer or the question was written wrong.<BR>\n" );
document.write( "x= 10.8488578017961 or -8.8488578017961<BR>\n" );
document.write( "(x+2)= 12.8488578017961 or -6.8488578017961<BR>\n" );
document.write( "(x+4)= 14.8488578017961 or -4.8488578017961<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=1x%5E2%2B-2x%2B-96+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-2x%2B-96+=+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=%28-2%29%5E2-4%2A1%2A-96=388 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-2%29%5E2-4%2A1%2A-96=388\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=388 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--2%2B-sqrt%28+388+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--2%2B-sqrt%28+388+%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-%28-2%29%2Bsqrt%28+388+%29%29%2F2%5C1+=+10.8488578017961 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+388+%29%29%2F2%5C1+=+10.8488578017961\"   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-%28-2%29-sqrt%28+388+%29%29%2F2%5C1+=+-8.8488578017961 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-2%29-sqrt%28+388+%29%29%2F2%5C1+=+-8.8488578017961\"   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%2B-2x%2B-96 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-2x%2B-96\"   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%2B-2x%2B-96+=+1%28x-10.8488578017961%29%2A%28x--8.8488578017961%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-2x%2B-96+=+1%28x-10.8488578017961%29%2A%28x--8.8488578017961%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 10.8488578017961, -8.8488578017961.\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-2%2Ax%2B-96+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-96+%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" );