document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=744694>Question 744694</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm having some trouble with a question on my test:<BR>\n" );
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document.write( "-11x^2+12x - 6 = 0<BR>\n" );
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document.write( "Answers:<BR>\n" );
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document.write( "A) x ={-6 +- i[SQRT(60)]}/11 <BR>\n" );
document.write( "B) x = {-6 +- i[SQRT(30)]}/-11 <BR>\n" );
document.write( "C) x = {6 +- i[SQRT(12)]}/6 <BR>\n" );
document.write( "D) x = {-6 +- i[SQRT(22)]}/-11 <BR>\n" );
document.write( "E) x = {-11 +- i} /6 <BR>\n" );
document.write( "F) x = {11 +- i} /-6 <BR>\n" );
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document.write( "What I did first is to insert the question into the quadratic formula, with -11, 12 and -6 as a, b and c.\r<BR>\n" );
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document.write( "(-12 ± &#8730;144 - 264) / (-22)<BR>\n" );
document.write( "Which turns into<BR>\n" );
document.write( "(-12±&#8730;-120) / -22<BR>\n" );
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document.write( "But now I'm stuck. Could I have some help please? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #453499 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=453499\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> -11x^2+12x - 6 = 0<BR>\n" );
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document.write( "Answers:<BR>\n" );
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document.write( "A) x ={-6 +- i[SQRT(60)]}/11 <BR>\n" );
document.write( "B) x = {-6 +- i[SQRT(30)]}/-11 <BR>\n" );
document.write( "C) x = {6 +- i[SQRT(12)]}/6 <BR>\n" );
document.write( "D) x = {-6 +- i[SQRT(22)]}/-11 <BR>\n" );
document.write( "E) x = {-11 +- i} /6 <BR>\n" );
document.write( "F) x = {11 +- i} /-6 <BR>\n" );
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document.write( "What I did first is to insert the question into the quadratic formula, with -11, 12 and -6 as a, b and c. <BR>\n" );
document.write( "(-12 ± &#8730;144 - 264) / (-22)<BR>\n" );
document.write( "Which turns into<BR>\n" );
document.write( "(-12±&#8730;-120) / -22<BR>\n" );
document.write( ".<BR>\n" );
document.write( "But now I'm stuck. Could I have some help please?<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "(-12±&#8730;-120) / -22  You were almost done.<BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286+%2B+i%2Asqrt%2830%29%29%2F11 ALIGN=MIDDLE  ALT=\"%286+%2B+i%2Asqrt%2830%29%29%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286+-+i%2Asqrt%2830%29%29%2F11 ALIGN=MIDDLE  ALT=\"%286+-+i%2Asqrt%2830%29%29%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--> C<BR>\n" );
document.write( "============<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=-11x%5E2%2B12x%2B-6+=+0 ALIGN=MIDDLE  ALT=\"-11x%5E2%2B12x%2B-6+=+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=%2812%29%5E2-4%2A-11%2A-6=-120 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2812%29%5E2-4%2A-11%2A-6=-120\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  The discriminant -120 is less than zero. That means that there are no solutions among real numbers.<BR><BR>\n" );
document.write( "  If you are a student of advanced school algebra and are aware about <u>imaginary numbers<u>, read on.<BR><BR>\n" );
document.write( "  <BR>\n" );
document.write( "      In the field of imaginary numbers, the square root of -120 is + or - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28+120%29+=+10.9544511501033 ALIGN=MIDDLE  ALT=\"sqrt%28+120%29+=+10.9544511501033\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "  <BR>\n" );
document.write( "      The solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28-12%2B-i%2Asqrt%28+-120+%29%29%2F2%5C-11+=++%28-12%2B-i%2A10.9544511501033%29%2F2%5C-11+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >, or<BR>\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+-11%2Ax%5E2%2B12%2Ax%2B-6+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-11%2Ax%5E2%2B12%2Ax%2B-6+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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