document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=952370>Question 952370</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find three consecutive even integers such that the product of the first and the third is 18 greater than the product of -1 and the third. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #581598 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=581598\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x=first x+2=second x+4=third<BR>\n" );
document.write( "(x)(x+4)=((-1)(x+4))+18<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4x=-x-4%2B18 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x=-x-4%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add x to each side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B5x=14 ALIGN=MIDDLE  ALT=\"x%5E2%2B5x=14\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 14 from each side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B5x-14=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B5x-14=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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=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%2B5x%2B-14+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B5x%2B-14+=+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=%285%29%5E2-4%2A1%2A-14=81 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%285%29%5E2-4%2A1%2A-14=81\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=81 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+=+%28-5%2B-sqrt%28+81+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-5%2B-sqrt%28+81+%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-%285%29%2Bsqrt%28+81+%29%29%2F2%5C1+=+2 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%285%29%2Bsqrt%28+81+%29%29%2F2%5C1+=+2\"   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-%285%29-sqrt%28+81+%29%29%2F2%5C1+=+-7 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%285%29-sqrt%28+81+%29%29%2F2%5C1+=+-7\"   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%2B5x%2B-14 ALIGN=MIDDLE  ALT=\"1x%5E2%2B5x%2B-14\"   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%2B5x%2B-14+=+1%28x-2%29%2A%28x--7%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B5x%2B-14+=+1%28x-2%29%2A%28x--7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 2, -7.\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%2B5%2Ax%2B-14+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B5%2Ax%2B-14+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "ANSWER 1: The first integer is 2.<BR>\n" );
document.write( "x+2=2+2=4 ANSWER 2: The second integer is 4.<BR>\n" );
document.write( "x+4=2+4=6 ANSWER 3: The third integer is 6.<BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "(2)(6)=-1(6)+18<BR>\n" );
document.write( "12=-6+18<BR>\n" );
document.write( "12=12 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );