document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=170968>Question 170968</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve each equation by using the quadratic formula.\r<BR>\n" );
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document.write( " 14. -8q^2 - 2q + 1 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #126218 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=126218\">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 q:<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=aq%5E2%2Bbq%2Bc=0 ALIGN=MIDDLE  ALT=\"aq%5E2%2Bbq%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=q+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"q+=+%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=-8%2Aq%5E2-2%2Aq%2B1=0 ALIGN=MIDDLE  ALT=\"-8%2Aq%5E2-2%2Aq%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-8 ALIGN=MIDDLE  ALT=\"a=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-2 ALIGN=MIDDLE  ALT=\"b=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=1 ALIGN=MIDDLE  ALT=\"c=1\"   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=q+=+%28--2+%2B-+sqrt%28+%28-2%29%5E2-4%2A-8%2A1+%29%29%2F%282%2A-8%29 ALIGN=MIDDLE  ALT=\"q+=+%28--2+%2B-+sqrt%28+%28-2%29%5E2-4%2A-8%2A1+%29%29%2F%282%2A-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=-8, b=-2, and c=1<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%2A-8%2A1+%29%29%2F%282%2A-8%29 ALIGN=MIDDLE  ALT=\"q+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%2A-8%2A1+%29%29%2F%282%2A-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -2 to get 2<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q+=+%282+%2B-+sqrt%28+4-4%2A-8%2A1+%29%29%2F%282%2A-8%29 ALIGN=MIDDLE  ALT=\"q+=+%282+%2B-+sqrt%28+4-4%2A-8%2A1+%29%29%2F%282%2A-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -2 to get 4  (note: remember when you square -2, you must square the negative as well. This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%29%5E2=-2%2A-2=4 ALIGN=MIDDLE  ALT=\"%28-2%29%5E2=-2%2A-2=4\"   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=q+=+%282+%2B-+sqrt%28+4%2B32+%29%29%2F%282%2A-8%29 ALIGN=MIDDLE  ALT=\"q+=+%282+%2B-+sqrt%28+4%2B32+%29%29%2F%282%2A-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A1%2A-8 ALIGN=MIDDLE  ALT=\"-4%2A1%2A-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32 ALIGN=MIDDLE  ALT=\"32\"   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=q+=+%282+%2B-+sqrt%28+36+%29%29%2F%282%2A-8%29 ALIGN=MIDDLE  ALT=\"q+=+%282+%2B-+sqrt%28+36+%29%29%2F%282%2A-8%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=q+=+%282+%2B-+6%29%2F%282%2A-8%29 ALIGN=MIDDLE  ALT=\"q+=+%282+%2B-+6%29%2F%282%2A-8%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=q+=+%282+%2B-+6%29%2F-16 ALIGN=MIDDLE  ALT=\"q+=+%282+%2B-+6%29%2F-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and -8 to get -16<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=q+=+%282+%2B+6%29%2F-16 ALIGN=MIDDLE  ALT=\"q+=+%282+%2B+6%29%2F-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q+=+%282+-+6%29%2F-16 ALIGN=MIDDLE  ALT=\"q+=+%282+-+6%29%2F-16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Lets look at the first part:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%282+%2B+6%29%2F-16 ALIGN=MIDDLE  ALT=\"x=%282+%2B+6%29%2F-16\"   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=q=8%2F-16 ALIGN=MIDDLE  ALT=\"q=8%2F-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add the terms in the numerator<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q=-1%2F2 ALIGN=MIDDLE  ALT=\"q=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide<BR>\n" );
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document.write( "  So one answer is<BR>\n" );
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document.write( "  Now lets look at the second part:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%282+-+6%29%2F-16 ALIGN=MIDDLE  ALT=\"x=%282+-+6%29%2F-16\"   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=q=-4%2F-16 ALIGN=MIDDLE  ALT=\"q=-4%2F-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract the terms in the numerator<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q=1%2F4 ALIGN=MIDDLE  ALT=\"q=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide<BR>\n" );
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document.write( "  So another answer is<BR>\n" );
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document.write( "  So our solutions are:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q=-1%2F2 ALIGN=MIDDLE  ALT=\"q=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q=1%2F4 ALIGN=MIDDLE  ALT=\"q=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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