document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=462630>Question 462630</A>: <I><SPAN STYLE=\"word-break: break-all;\"> f(x)=x^(2)-6x-2 how to solve </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #317144 by </B><A HREF=/tutors/aboutme.mpl?userid=math-vortex><B>math-vortex(648)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math-vortex><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=math-vortex><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=317144\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve f(x)=x^(2)-6x-2<BR>\n" );
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document.write( "When you say, \"solve,\" I'm thinking that you want to know the values of x where f(x)=0.<BR>\n" );
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document.write( "Let f(x) = 0. Then we have<BR>\n" );
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document.write( "x^2 - 6x - 2 = 0<BR>\n" );
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document.write( "This is a quadratic equation, so we have two solution methods available: we can use the factoring method, or we can apply the quadratic formula. I don't see an obvious way to factor the left-hand side, so we'll use the quadratic formula.<BR>\n" );
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document.write( "The equation is already in the general (standard) form, <BR>\n" );
document.write( "ax^2 + bx + c = 0<BR>\n" );
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document.write( "We have<BR>\n" );
document.write( "a = 1<BR>\n" );
document.write( "b = -6<BR>\n" );
document.write( "c = -2<BR>\n" );
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document.write( "Now, we apply the quadratic formula,<BR>\n" );
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;\" ><BR>\n" );
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document.write( "We substitute the values for a, b, and c from our quadratic equation into the formula.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-6%29%2B-sqrt%28%28-6%29%5E2-4%281%29%28-2%29%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-6%29%2B-sqrt%28%28-6%29%5E2-4%281%29%28-2%29%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now we simplify,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%286%2B-sqrt%2836%2B8%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%286%2B-sqrt%2836%2B8%29%29%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=x+=+%286%2B-sqrt%2844%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%286%2B-sqrt%2844%29%29%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=x+=+%286%2B-2%2A%28sqrt%2811%29%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%286%2B-2%2A%28sqrt%2811%29%29%29%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=x+=+3%2B-sqrt%2811%29 ALIGN=MIDDLE  ALT=\"x+=+3%2B-sqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The \"plus or minus\" in the formula give us two roots; either <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3%2Bsqrt%2811%29 ALIGN=MIDDLE  ALT=\"x+=+3%2Bsqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3-sqrt%2811%29 ALIGN=MIDDLE  ALT=\"x+=+3-sqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Here is a graph of your equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+450%2C+300%2C+-5%2C+12%2C+-12%2C+5%2C+x%5E2-6x-2+%29 ALIGN=MIDDLE  ALT=\"graph%28+450%2C+300%2C+-5%2C+12%2C+-12%2C+5%2C+x%5E2-6x-2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "hope this helps! If you have questions, feel free to email me at math.in.the.vortex@gmail.com<BR>\n" );
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document.write( "Ms.Figgy<BR>\n" );
document.write( "math.in.the.vortex </SPAN>\n" );
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