document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=419764>Question 419764</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve using the quadratic formula and leave the answer in radical form? Could you show work as I am very confused. Thanks.<BR>\n" );
document.write( "Karyn\r<BR>\n" );
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document.write( "y^2+6y-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 #293462 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=293462\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> equation is:\r<BR>\n" );
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document.write( "y^2 + 6y - 1 = 0\r<BR>\n" );
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document.write( "standard form of a quadratic equation is:\r<BR>\n" );
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document.write( "ax^2 + bx + c = 0\r<BR>\n" );
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document.write( "a is the coefficient of the x^2 term.<BR>\n" );
document.write( "b is the coefficient of the x term.<BR>\n" );
document.write( "c is the constant.\r<BR>\n" );
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document.write( "in your equation you have:\r<BR>\n" );
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document.write( "a = 1<BR>\n" );
document.write( "b = 6<BR>\n" );
document.write( "c = -1\r<BR>\n" );
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document.write( "the quadratic formula is:\r<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%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you replace the a's and the b's and the c's with their respective values to get:\r<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%286%5E2-4%2A1%2A-1%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+sqrt%286%5E2-4%2A1%2A-1%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the * is the multiplication symbol.\r<BR>\n" );
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document.write( "in the formula you see it looks like a little square.\r<BR>\n" );
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document.write( "I typed a *.   The formula generator program converted it to a little square.\r<BR>\n" );
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document.write( "you would simplify this expression to be shown as follows:\r<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%2840%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+sqrt%2840%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "it can also be simplified further to be shown as:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-3%29+%2B-+sqrt%2840%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%28-3%29+%2B-+sqrt%2840%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "it can even be simplified further to be shown as:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-3%29+%2B-+sqrt%2810%29 ALIGN=MIDDLE  ALT=\"x+=+%28-3%29+%2B-+sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2840%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%2840%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the same thing as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2810%29 ALIGN=MIDDLE  ALT=\"sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2840%29 ALIGN=MIDDLE  ALT=\"sqrt%2840%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > equals <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%2A2%2A10%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%282%2A2%2A10%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which equals <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%2810%29%2F2 ALIGN=MIDDLE  ALT=\"2%2Asqrt%2810%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which equals <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2810%29 ALIGN=MIDDLE  ALT=\"sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "since they only told you to leave the answer in radical form, then i suspect you're ok with any of the answers that still have a radical in them.\r<BR>\n" );
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document.write( "that's between you and your teacher as to how he/she wants to see the answer.\r<BR>\n" );
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document.write( "a graph of your equation looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C10%2C-20%2C20%2Cx%5E2+%2B+6x+-+1%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C10%2C-20%2C20%2Cx%5E2+%2B+6x+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you can see that the graph crosses the x-axis somewhere around x = -6.16 and x = .16 which is where the equation of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-3%29+%2B-+sqrt%2810%29 ALIGN=MIDDLE  ALT=\"x+=+%28-3%29+%2B-+sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > indicates.\r<BR>\n" );
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document.write( "note that sqrt(10) is somewhere around 3.16...\r<BR>\n" );
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