document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=699126>Question 699126</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the sum of two numbers is 30. if the larger number is divided by the smaller number the quotient is equal to the smaller number. find the numbers.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #431228 by </B><A HREF=/tutors/aboutme.mpl?userid=Stitch><B>Stitch(470)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Stitch><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=431228\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Equation 1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+%2B+B+=+30 ALIGN=MIDDLE  ALT=\"A+%2B+B+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Equation 2:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2FB+=+B ALIGN=MIDDLE  ALT=\"A%2FB+=+B\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solve equation 2 for A by multiplying both sides by B<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+B%5E2 ALIGN=MIDDLE  ALT=\"A+=+B%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now plug B^2 into equation 1 for A<BR>\n" );
document.write( "Equation 1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+%2B+B+=+30 ALIGN=MIDDLE  ALT=\"A+%2B+B+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28B%5E2%29+%2B+B+=+30 ALIGN=MIDDLE  ALT=\"%28B%5E2%29+%2B+B+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 30 from both sides to set the equation equal to zero<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%5E2+%2B+B+-+30+=+0 ALIGN=MIDDLE  ALT=\"B%5E2+%2B+B+-+30+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now you can use the quadratic equation<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=aB%5E2%2BbB%2Bc=0 ALIGN=MIDDLE  ALT=\"aB%5E2%2BbB%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1B%5E2%2B1B%2B-30+=+0 ALIGN=MIDDLE  ALT=\"1B%5E2%2B1B%2B-30+=+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=B%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"B%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=%281%29%5E2-4%2A1%2A-30=121 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%281%29%5E2-4%2A1%2A-30=121\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=121 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+=+%28-1%2B-sqrt%28+121+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-1%2B-sqrt%28+121+%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=B%5B1%5D+=+%28-%281%29%2Bsqrt%28+121+%29%29%2F2%5C1+=+5 ALIGN=MIDDLE  ALT=\"B%5B1%5D+=+%28-%281%29%2Bsqrt%28+121+%29%29%2F2%5C1+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%5B2%5D+=+%28-%281%29-sqrt%28+121+%29%29%2F2%5C1+=+-6 ALIGN=MIDDLE  ALT=\"B%5B2%5D+=+%28-%281%29-sqrt%28+121+%29%29%2F2%5C1+=+-6\"   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=1B%5E2%2B1B%2B-30 ALIGN=MIDDLE  ALT=\"1B%5E2%2B1B%2B-30\"   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=1B%5E2%2B1B%2B-30+=+1%28B-5%29%2A%28B--6%29 ALIGN=MIDDLE  ALT=\"1B%5E2%2B1B%2B-30+=+1%28B-5%29%2A%28B--6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 5, -6.\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%2B1%2Ax%2B-30+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-30+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "Note that B can equal 5 or -6. <BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "Plug 5 into equation 1 for B<BR>\n" );
document.write( "Equation 1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+%2B+B+=+30 ALIGN=MIDDLE  ALT=\"A+%2B+B+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+%2B+%285%29+=+30 ALIGN=MIDDLE  ALT=\"A+%2B+%285%29+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 5 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28A+=+25%29 ALIGN=MIDDLE  ALT=\"highlight%28A+=+25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Check your answer:<BR>\n" );
document.write( "5 + 25 = 30 That checks<BR>\n" );
document.write( "25 / 5 = 5 That checks<BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "Plug -6 into equation 1 for B<BR>\n" );
document.write( "Equation 1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+%2B+B+=+30 ALIGN=MIDDLE  ALT=\"A+%2B+B+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+%2B+%28-6%29+=+30 ALIGN=MIDDLE  ALT=\"A+%2B+%28-6%29+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Add 6 to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28A+=+36%29 ALIGN=MIDDLE  ALT=\"highlight%28A+=+36%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Check your answer:<BR>\n" );
document.write( "-6 + 36 = 30 That checks<BR>\n" );
document.write( "36 / -6 = -6 That checks<BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "So for this problem you have two answers: 5 & 25, or -6 and 36<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );