document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1016156>Question 1016156</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of a number and 8, mulitipled by the sum of the number and 5 is equivalent to 19. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #632555 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=632555\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "You did not ask a question.<BR>\n" );
document.write( "Assuming you want to find the number.<BR>\n" );
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document.write( "x=the number<BR>\n" );
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document.write( "(x+8)(x+5)=19<BR>\n" );
document.write( "x^2+13x+40=19<BR>\n" );
document.write( "x^2+13x+21=0<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%2B13x%2B21+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B13x%2B21+=+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=%2813%29%5E2-4%2A1%2A21=85 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2813%29%5E2-4%2A1%2A21=85\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=85 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+=+%28-13%2B-sqrt%28+85+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-13%2B-sqrt%28+85+%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-%2813%29%2Bsqrt%28+85+%29%29%2F2%5C1+=+-1.89022777135356 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2813%29%2Bsqrt%28+85+%29%29%2F2%5C1+=+-1.89022777135356\"   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-%2813%29-sqrt%28+85+%29%29%2F2%5C1+=+-11.1097722286464 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2813%29-sqrt%28+85+%29%29%2F2%5C1+=+-11.1097722286464\"   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%2B13x%2B21 ALIGN=MIDDLE  ALT=\"1x%5E2%2B13x%2B21\"   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%2B13x%2B21+=+1%28x--1.89022777135356%29%2A%28x--11.1097722286464%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B13x%2B21+=+1%28x--1.89022777135356%29%2A%28x--11.1097722286464%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -1.89022777135356, -11.1097722286464.\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%2B13%2Ax%2B21+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B13%2Ax%2B21+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "ANSWER: The number is -1.89 or -11.11.<BR>\n" );
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document.write( "CHECK:<BR>\n" );
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document.write( "For x=-1.89<BR>\n" );
document.write( "(x+8)(x+5)=19<BR>\n" );
document.write( "(-1.89+8)(-1.89+5)=19<BR>\n" );
document.write( "(6.11)(3.11)=19<BR>\n" );
document.write( "19=19<BR>\n" );
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document.write( "For -11.11<BR>\n" );
document.write( "(-11.11+8)(-11.11+5)=19<BR>\n" );
document.write( "(-3.11)(-6.11)=19<BR>\n" );
document.write( "19=19<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );