document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=396646>Question 396646</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the sum of 2 numbers is -14 and their product is 32, what are the numbers?\r<BR>\n" );
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document.write( "Let x = one number<BR>\n" );
document.write( "Let x - 14 = the other number\r<BR>\n" );
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document.write( "x(x - 14) = 32<BR>\n" );
document.write( "x^2- 14x + 32\r<BR>\n" );
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document.write( "(x - 6) (x-8) \r<BR>\n" );
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document.write( "The two numbers are -8 and -6<BR>\n" );
document.write( "I know that -8 + -6 = -14 but when I plug in the numbers that do not equal 32.  What am I not doing correct? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #281315 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=281315\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the sum of 2 numbers is -14 and their product is 32, what are the numbers?\r<BR>\n" );
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document.write( "Let x = one number<BR>\n" );
document.write( "Let x - 14 = the other number\r<BR>\n" );
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document.write( "x(x - 14) = 32<BR>\n" );
document.write( "x^2- 14x + 32\r<BR>\n" );
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document.write( "(x - 6) (x-8) \r<BR>\n" );
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document.write( "The two numbers are -8 and -6<BR>\n" );
document.write( "I know that -8 + -6 = -14 but when I plug in the numbers that do not equal 32.  What am I not doing correct?<BR>\n" );
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document.write( "Let x = one number<BR>\n" );
document.write( "Let -14 - x = the other number\r<BR>\n" );
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document.write( "x(-x - 14) = 32<BR>\n" );
document.write( "-x^2 - 14x - 32 = 0<BR>\n" );
document.write( "x^2 + 14x + 32 = 0<BR>\n" );
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=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</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%2B14x%2B32+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B14x%2B32+=+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=%2814%29%5E2-4%2A1%2A32=68 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2814%29%5E2-4%2A1%2A32=68\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=68 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+=+%28-14%2B-sqrt%28+68+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-14%2B-sqrt%28+68+%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-%2814%29%2Bsqrt%28+68+%29%29%2F2%5C1+=+-2.87689437438234 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2814%29%2Bsqrt%28+68+%29%29%2F2%5C1+=+-2.87689437438234\"   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-%2814%29-sqrt%28+68+%29%29%2F2%5C1+=+-11.1231056256177 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2814%29-sqrt%28+68+%29%29%2F2%5C1+=+-11.1231056256177\"   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%2B14x%2B32 ALIGN=MIDDLE  ALT=\"1x%5E2%2B14x%2B32\"   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%2B14x%2B32+=+%28x--2.87689437438234%29%2A%28x--11.1231056256177%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B14x%2B32+=+%28x--2.87689437438234%29%2A%28x--11.1231056256177%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -2.87689437438234, -11.1231056256177.\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%2B14%2Ax%2B32+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B14%2Ax%2B32+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "x = -7 ± sqrt(17)<BR>\n" );
document.write( "One number is -7 + sqrt, the other is -7 - sqrt<BR>\n" );
document.write( "No integer solutions.<BR>\n" );
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document.write( "I would check for a typo.<BR>\n" );
document.write( "If the sum is -12, then it's -4 and -8. </SPAN>\n" );
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