document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=877076>Question 877076</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 30m^2-77m-10=0<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #529171 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=529171\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <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_formula.solver>Quadratic Formula</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Let's use the quadratic formula to solve for m:<BR><BR>\n" );
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document.write( "  Starting with the general quadratic<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=am%5E2%2Bbm%2Bc=0 ALIGN=MIDDLE  ALT=\"am%5E2%2Bbm%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  the general solution using the quadratic equation is:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"m+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2Am%5E2-77%2Am-10=0 ALIGN=MIDDLE  ALT=\"30%2Am%5E2-77%2Am-10=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=30 ALIGN=MIDDLE  ALT=\"a=30\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-77 ALIGN=MIDDLE  ALT=\"b=-77\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-10 ALIGN=MIDDLE  ALT=\"c=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28--77+%2B-+sqrt%28+%28-77%29%5E2-4%2A30%2A-10+%29%29%2F%282%2A30%29 ALIGN=MIDDLE  ALT=\"m+=+%28--77+%2B-+sqrt%28+%28-77%29%5E2-4%2A30%2A-10+%29%29%2F%282%2A30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=30, b=-77, and c=-10<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%2877+%2B-+sqrt%28+%28-77%29%5E2-4%2A30%2A-10+%29%29%2F%282%2A30%29 ALIGN=MIDDLE  ALT=\"m+=+%2877+%2B-+sqrt%28+%28-77%29%5E2-4%2A30%2A-10+%29%29%2F%282%2A30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -77 to get 77<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%2877+%2B-+sqrt%28+5929-4%2A30%2A-10+%29%29%2F%282%2A30%29 ALIGN=MIDDLE  ALT=\"m+=+%2877+%2B-+sqrt%28+5929-4%2A30%2A-10+%29%29%2F%282%2A30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -77 to get 5929  (note: remember when you square -77, you must square the negative as well. This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-77%29%5E2=-77%2A-77=5929 ALIGN=MIDDLE  ALT=\"%28-77%29%5E2=-77%2A-77=5929\"   DISABLED_style= \"max-width:90%; height:auto;\" >.)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%2877+%2B-+sqrt%28+5929%2B1200+%29%29%2F%282%2A30%29 ALIGN=MIDDLE  ALT=\"m+=+%2877+%2B-+sqrt%28+5929%2B1200+%29%29%2F%282%2A30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A-10%2A30 ALIGN=MIDDLE  ALT=\"-4%2A-10%2A30\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1200 ALIGN=MIDDLE  ALT=\"1200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%2877+%2B-+sqrt%28+7129+%29%29%2F%282%2A30%29 ALIGN=MIDDLE  ALT=\"m+=+%2877+%2B-+sqrt%28+7129+%29%29%2F%282%2A30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%2877+%2B-+sqrt%287129%29%29%2F%282%2A30%29 ALIGN=MIDDLE  ALT=\"m+=+%2877+%2B-+sqrt%287129%29%29%2F%282%2A30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%2877+%2B-+sqrt%287129%29%29%2F60 ALIGN=MIDDLE  ALT=\"m+=+%2877+%2B-+sqrt%287129%29%29%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 30 to get 60<BR>\n" );
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document.write( "  So now the expression breaks down into two parts<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%2877+%2B+sqrt%287129%29%29%2F60 ALIGN=MIDDLE  ALT=\"m+=+%2877+%2B+sqrt%287129%29%29%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%2877+-+sqrt%287129%29%29%2F60 ALIGN=MIDDLE  ALT=\"m+=+%2877+-+sqrt%287129%29%29%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Now break up the fraction<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%2B77%2F60%2Bsqrt%287129%29%2F60 ALIGN=MIDDLE  ALT=\"m=%2B77%2F60%2Bsqrt%287129%29%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%2B77%2F60-sqrt%287129%29%2F60 ALIGN=MIDDLE  ALT=\"m=%2B77%2F60-sqrt%287129%29%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Simplify<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=77%2F60%2Bsqrt%287129%29%2F60 ALIGN=MIDDLE  ALT=\"m=77%2F60%2Bsqrt%287129%29%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=77%2F60-sqrt%287129%29%2F60 ALIGN=MIDDLE  ALT=\"m=77%2F60-sqrt%287129%29%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  So the solutions are:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=77%2F60%2Bsqrt%287129%29%2F60 ALIGN=MIDDLE  ALT=\"m=77%2F60%2Bsqrt%287129%29%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=77%2F60-sqrt%287129%29%2F60 ALIGN=MIDDLE  ALT=\"m=77%2F60-sqrt%287129%29%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note: You can also write the final answers as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%2877%2Bsqrt%287129%29%29%2F60 ALIGN=MIDDLE  ALT=\"m+=+%2877%2Bsqrt%287129%29%29%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%2877-sqrt%287129%29%29%2F60 ALIGN=MIDDLE  ALT=\"m+=+%2877-sqrt%287129%29%29%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You can condense that into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%2877%2B-sqrt%287129%29%29%2F60 ALIGN=MIDDLE  ALT=\"m+=+%2877%2B-sqrt%287129%29%29%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "These are exact answers. To find the approximate answers, use a calculator to evaluate the expressions. </SPAN>\n" );
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