document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=164959>Question 164959</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780073533490/algebrahomeworkh>Elementary and Intermediate</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 14.) Solve each equation by using the quadratic formula\r<BR>\n" );
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document.write( "-8q^2-2q+1=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 #121580 by </B><A HREF=/tutors/aboutme.mpl?userid=Electrified_Levi><B>Electrified_Levi(103)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Electrified_Levi><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=121580\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, Hope I can help,<BR>\n" );
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document.write( "14.) Solve each equation by using the quadratic formula <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-8q%5E2-2q%2B1=0+ ALIGN=MIDDLE  ALT=\"+-8q%5E2-2q%2B1=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "First we have to but the equation in the standard form <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;\" ><BR>\n" );
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document.write( "It is already in that form. (x is replaced with q)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-8q%5E2-2q%2B1=0+ ALIGN=MIDDLE  ALT=\"+-8q%5E2-2q%2B1=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <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( "A = (-8)<BR>\n" );
document.write( "B = (-2)<BR>\n" );
document.write( "C = 1<BR>\n" );
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document.write( "We have to know the quadratic equation, which 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( "We can replace A with (-8), B with (-2), C with \"1\"<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;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%2A%28-8%29%2A%281%29+%29%29%2F%282%2A%28-8%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q+=+%28%282+%2B-+sqrt%28+4-%28-32%29+%29%29%2F%28-16%29%29+ ALIGN=MIDDLE  ALT=\"q+=+%28%282+%2B-+sqrt%28+4-%28-32%29+%29%29%2F%28-16%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q+=+%28%282+%2B-+sqrt%28+4%2B+32+%29%29%2F%28-16%29%29+ ALIGN=MIDDLE  ALT=\"q+=+%28%282+%2B-+sqrt%28+4%2B+32+%29%29%2F%28-16%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q+=+%28%282+%2B-+sqrt%28+36+%29%29%2F%28-16%29%29+ ALIGN=MIDDLE  ALT=\"q+=+%28%282+%2B-+sqrt%28+36+%29%29%2F%28-16%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q+=+%28%282+%2B-+6%29%2F%28-16%29%29+ ALIGN=MIDDLE  ALT=\"q+=+%28%282+%2B-+6%29%2F%28-16%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "There are two answers that \"q\" can equal ( + 6, - 6 )<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q+=+%28%282+%2B+6%29%2F%28-16%29%29+ ALIGN=MIDDLE  ALT=\"q+=+%28%282+%2B+6%29%2F%28-16%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q+=+8%2F%28-16%29+ ALIGN=MIDDLE  ALT=\"q+=+8%2F%28-16%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <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;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q+=+%28%282+-+6%29%2F%28-16%29%29+ ALIGN=MIDDLE  ALT=\"q+=+%28%282+-+6%29%2F%28-16%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q+=+%28-4%29%2F%28-16%29+ ALIGN=MIDDLE  ALT=\"q+=+%28-4%29%2F%28-16%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <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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document.write( "q can be  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-1%2F2+ ALIGN=MIDDLE  ALT=\"+-1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F4+ ALIGN=MIDDLE  ALT=\"+1%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "You can check by replacing \"q\" with \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\", and \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\" in the original equation, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-8q%5E2-2q%2B1=0+ ALIGN=MIDDLE  ALT=\"+-8q%5E2-2q%2B1=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "q = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-1%2F2+ ALIGN=MIDDLE  ALT=\"+-1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-8q%5E2-2q%2B1=0+ ALIGN=MIDDLE  ALT=\"+-8q%5E2-2q%2B1=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-8%28-1%2F2%29%5E2-2%28-1%2F2%29%2B1=0+ ALIGN=MIDDLE  ALT=\"+-8%28-1%2F2%29%5E2-2%28-1%2F2%29%2B1=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-8%281%2F4%29-%28-1%29%2B1=0+ ALIGN=MIDDLE  ALT=\"+-8%281%2F4%29-%28-1%29%2B1=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-2%29%2B1%2B1=0+ ALIGN=MIDDLE  ALT=\"+%28-2%29%2B1%2B1=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-2%29%2B2=0+ ALIGN=MIDDLE  ALT=\"+%28-2%29%2B2=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0=0+ ALIGN=MIDDLE  ALT=\"+0=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (True)<BR>\n" );
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document.write( "q = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-8q%5E2-2q%2B1=0+ ALIGN=MIDDLE  ALT=\"+-8q%5E2-2q%2B1=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-8%281%2F4%29%5E2-2%281%2F4%29%2B1=0+ ALIGN=MIDDLE  ALT=\"+-8%281%2F4%29%5E2-2%281%2F4%29%2B1=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-8%281%2F16%29-%282%2F4%29%2B1=0+ ALIGN=MIDDLE  ALT=\"+-8%281%2F16%29-%282%2F4%29%2B1=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-8%2F16%29-%282%2F4%29%2B1=0+ ALIGN=MIDDLE  ALT=\"+%28-8%2F16%29-%282%2F4%29%2B1=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-1%2F2%29-+%281%2F2%29%2B1=0+ ALIGN=MIDDLE  ALT=\"+%28-1%2F2%29-+%281%2F2%29%2B1=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-1%29%2B1+=+0+ ALIGN=MIDDLE  ALT=\"+%28-1%29%2B1+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0=0+ ALIGN=MIDDLE  ALT=\"+0=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (True)<BR>\n" );
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document.write( "q =  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-1%2F2+ ALIGN=MIDDLE  ALT=\"+-1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "q =   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F4+ ALIGN=MIDDLE  ALT=\"+1%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "Here is the graph of the equation<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing+%28+600%2C600%2C-10%2C10%2C-10%2C10%2Cgrid%281%29%2C+graph+%28+600%2C600%2C-10%2C10%2C-10%2C10%2C+-8x%5E2-2x%2B1+%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Where the curved line crosses the x axis, are the solutions to the equation<BR>\n" );
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document.write( "The curved line crosses where \"q\"(or \"x\") =  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-1%2F2+ ALIGN=MIDDLE  ALT=\"+-1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > , it also crosses the x axis where \"q\"(or \"x\") = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F4+ ALIGN=MIDDLE  ALT=\"+1%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The two solutions are<BR>\n" );
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document.write( "q = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-1%2F2+ ALIGN=MIDDLE  ALT=\"+-1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "q = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F4+ ALIGN=MIDDLE  ALT=\"+1%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope I helped, Levi <BR>\n" );
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