document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=170625>Question 170625</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618044302/algebrahomeworkh>Algebra structure and method book one</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following problem: The sum of the squares of two consecutive positve even integers is 340. Find the integers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #125938 by </B><A HREF=/tutors/aboutme.mpl?userid=Mathtut><B>Mathtut(3670)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mathtut><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=125938\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> two consecutive positive even integers we will call a and a+2<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2B%28a%2B2%29%5E2=340 ALIGN=MIDDLE  ALT=\"a%5E2%2B%28a%2B2%29%5E2=340\"   DISABLED_style= \"max-width:90%; height:auto;\" > distribute<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Ba%5E2%2B4a%2B4=340 ALIGN=MIDDLE  ALT=\"a%5E2%2Ba%5E2%2B4a%2B4=340\"   DISABLED_style= \"max-width:90%; height:auto;\" > combine a write as a quadratic <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%5E2%2B4a-336=0 ALIGN=MIDDLE  ALT=\"2a%5E2%2B4a-336=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > divide by 2<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2B2a-168=0 ALIGN=MIDDLE  ALT=\"a%5E2%2B2a-168=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a=12%2Ca=-14%29 ALIGN=MIDDLE  ALT=\"system%28a=12%2Ca=-14%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "throw out the negative value since we are looking for positive<BR>\n" );
document.write( "so the integers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%2812%2C14%29 ALIGN=MIDDLE  ALT=\"system%2812%2C14%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<TABLE  BORDER=1>\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=aa%5E2%2Bba%2Bc=0 ALIGN=MIDDLE  ALT=\"aa%5E2%2Bba%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1a%5E2%2B2a%2B-168+=+0 ALIGN=MIDDLE  ALT=\"1a%5E2%2B2a%2B-168+=+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=a%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"a%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=%282%29%5E2-4%2A1%2A-168=676 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%282%29%5E2-4%2A1%2A-168=676\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=676 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+676+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-2%2B-sqrt%28+676+%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=a%5B1%5D+=+%28-%282%29%2Bsqrt%28+676+%29%29%2F2%5C1+=+12 ALIGN=MIDDLE  ALT=\"a%5B1%5D+=+%28-%282%29%2Bsqrt%28+676+%29%29%2F2%5C1+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D+=+%28-%282%29-sqrt%28+676+%29%29%2F2%5C1+=+-14 ALIGN=MIDDLE  ALT=\"a%5B2%5D+=+%28-%282%29-sqrt%28+676+%29%29%2F2%5C1+=+-14\"   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=1a%5E2%2B2a%2B-168 ALIGN=MIDDLE  ALT=\"1a%5E2%2B2a%2B-168\"   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=1a%5E2%2B2a%2B-168+=+1%28a-12%29%2A%28a--14%29 ALIGN=MIDDLE  ALT=\"1a%5E2%2B2a%2B-168+=+1%28a-12%29%2A%28a--14%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 12, -14.\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%2B2%2Ax%2B-168+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-168+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );