document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=874285>Question 874285</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help!\r<BR>\n" );
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document.write( "Determine the number of real solutions of -x^2 -6x - 12=0 \r<BR>\n" );
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document.write( "Use the quadratic formula to find the exact values of the real solutions, if they exist. Give the solution Set.\r<BR>\n" );
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document.write( "Use a calculator to find approximations for the answers. Round your answers to the nearest thousandth. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #527423 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=527423\">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 x:<BR><BR>\n" );
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document.write( "  Starting with the general quadratic<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=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"x+=+%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=-x%5E2-6%2Ax-12=0 ALIGN=MIDDLE  ALT=\"-x%5E2-6%2Ax-12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-1 ALIGN=MIDDLE  ALT=\"a=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-6 ALIGN=MIDDLE  ALT=\"b=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-12 ALIGN=MIDDLE  ALT=\"c=-12\"   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=x+=+%28--6+%2B-+sqrt%28+%28-6%29%5E2-4%2A-1%2A-12+%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"x+=+%28--6+%2B-+sqrt%28+%28-6%29%5E2-4%2A-1%2A-12+%29%29%2F%282%2A-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=-1, b=-6, and c=-12<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%2A-1%2A-12+%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%2A-1%2A-12+%29%29%2F%282%2A-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -6 to get 6<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%286+%2B-+sqrt%28+36-4%2A-1%2A-12+%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"x+=+%286+%2B-+sqrt%28+36-4%2A-1%2A-12+%29%29%2F%282%2A-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -6 to get 36  (note: remember when you square -6, you must square the negative as well. This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-6%29%5E2=-6%2A-6=36 ALIGN=MIDDLE  ALT=\"%28-6%29%5E2=-6%2A-6=36\"   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=x+=+%286+%2B-+sqrt%28+36%2B-48+%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"x+=+%286+%2B-+sqrt%28+36%2B-48+%29%29%2F%282%2A-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A-12%2A-1 ALIGN=MIDDLE  ALT=\"-4%2A-12%2A-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-48 ALIGN=MIDDLE  ALT=\"-48\"   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=x+=+%286+%2B-+sqrt%28+-12+%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"x+=+%286+%2B-+sqrt%28+-12+%29%29%2F%282%2A-1%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=x+=+%286+%2B-+2%2Ai%2Asqrt%283%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"x+=+%286+%2B-+2%2Ai%2Asqrt%283%29%29%2F%282%2A-1%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=x+=+%286+%2B-+2%2Ai%2Asqrt%283%29%29%2F%28-2%29 ALIGN=MIDDLE  ALT=\"x+=+%286+%2B-+2%2Ai%2Asqrt%283%29%29%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and -1 to get -2<BR>\n" );
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document.write( "  After simplifying, the quadratic has roots of<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3-sqrt%283%29i ALIGN=MIDDLE  ALT=\"x=-3-sqrt%283%29i\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2Bsqrt%283%29i ALIGN=MIDDLE  ALT=\"x=-3%2Bsqrt%283%29i\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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