document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=112286>Question 112286</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find all real and/or imaginary solutions: 16xSQUARED + 48x + 40 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #81904 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=81904\">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=16%2Ax%5E2%2B48%2Ax%2B40=0 ALIGN=MIDDLE  ALT=\"16%2Ax%5E2%2B48%2Ax%2B40=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=16 ALIGN=MIDDLE  ALT=\"a=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=48 ALIGN=MIDDLE  ALT=\"b=48\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=40 ALIGN=MIDDLE  ALT=\"c=40\"   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+=+%28-48+%2B-+sqrt%28+%2848%29%5E2-4%2A16%2A40+%29%29%2F%282%2A16%29 ALIGN=MIDDLE  ALT=\"x+=+%28-48+%2B-+sqrt%28+%2848%29%5E2-4%2A16%2A40+%29%29%2F%282%2A16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=16, b=48, and c=40<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-48+%2B-+sqrt%28+2304-4%2A16%2A40+%29%29%2F%282%2A16%29 ALIGN=MIDDLE  ALT=\"x+=+%28-48+%2B-+sqrt%28+2304-4%2A16%2A40+%29%29%2F%282%2A16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 48 to get 2304  <BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-48+%2B-+sqrt%28+2304%2B-2560+%29%29%2F%282%2A16%29 ALIGN=MIDDLE  ALT=\"x+=+%28-48+%2B-+sqrt%28+2304%2B-2560+%29%29%2F%282%2A16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A40%2A16 ALIGN=MIDDLE  ALT=\"-4%2A40%2A16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2560 ALIGN=MIDDLE  ALT=\"-2560\"   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+=+%28-48+%2B-+sqrt%28+-256+%29%29%2F%282%2A16%29 ALIGN=MIDDLE  ALT=\"x+=+%28-48+%2B-+sqrt%28+-256+%29%29%2F%282%2A16%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+=+%28-48+%2B-+16%2Ai%29%2F%282%2A16%29 ALIGN=MIDDLE  ALT=\"x+=+%28-48+%2B-+16%2Ai%29%2F%282%2A16%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+=+%28-48+%2B-+16%2Ai%29%2F%2832%29 ALIGN=MIDDLE  ALT=\"x+=+%28-48+%2B-+16%2Ai%29%2F%2832%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 16 to get 32<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%2F2%2B1%2F2%2Ai ALIGN=MIDDLE  ALT=\"x=-3%2F2%2B1%2F2%2Ai\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2F2-1%2F2%2Ai ALIGN=MIDDLE  ALT=\"x=-3%2F2-1%2F2%2Ai\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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