document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=271137>Question 271137</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you solve this quadratic equation???<BR>\n" );
document.write( "x squared -17x-9=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #198539 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=198539\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> equation is x^2 - 17x - 9 = 0\r<BR>\n" );
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document.write( "it cannot be factored without using the quadratic formula or the completing the squares method.\r<BR>\n" );
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document.write( "quadratic formula method is:\r<BR>\n" );
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document.write( "x = quadratic formula is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"%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( "equation has to be in standard form of ax^2 + bx + c = 0 which it is.\r<BR>\n" );
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document.write( "a = 1<BR>\n" );
document.write( "b = -17<BR>\n" );
document.write( "c = -9\r<BR>\n" );
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document.write( "substitute in quadratic formula to get:\r<BR>\n" );
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document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-%28-17%29+%2B-+sqrt%28%28-17%29%5E2-4%2A1%2A%28-9%29%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"%28-%28-17%29+%2B-+sqrt%28%28-17%29%5E2-4%2A1%2A%28-9%29%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2817+%2B-+sqrt%28289%2B36%29%29%2F2 ALIGN=MIDDLE  ALT=\"%2817+%2B-+sqrt%28289%2B36%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2817+%2B-+sqrt%28325%29%29%2F2 ALIGN=MIDDLE  ALT=\"%2817+%2B-+sqrt%28325%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2817+%2B-+18.02775638%29%2F2 ALIGN=MIDDLE  ALT=\"%2817+%2B-+18.02775638%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "x = 17.51387819\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "x = -.0513878189\r<BR>\n" );
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document.write( "substitute in your original equation to confirm the answers are good.\r<BR>\n" );
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document.write( "your original equation is:\r<BR>\n" );
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document.write( "x^2 - 17x - 9 = 0\r<BR>\n" );
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document.write( "substituting 17.5387819 for x gets 0 = 0 so the first answer is good.\r<BR>\n" );
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document.write( "substituting -.5138978189 for x gets 0 = 0 so the second answer is good.\r<BR>\n" );
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document.write( "those are your factors.\r<BR>\n" );
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document.write( "completing the squares method works as follows:\r<BR>\n" );
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document.write( "your original equation is\r<BR>\n" );
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document.write( "x^2 - 17x - 9 = 0\r<BR>\n" );
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document.write( "add 9 to both sides of the equation to get\r<BR>\n" );
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document.write( "x^2 - 17x = 9\r<BR>\n" );
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document.write( "take 1/2 of the b term to get:\r<BR>\n" );
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document.write( "b/2 = -17/2 = -8.5\r<BR>\n" );
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document.write( "square that to get (b/2)^2 = 72.25\r<BR>\n" );
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document.write( "your completing the squares formula is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-8.5%29%5E2+=+9+%2B+72.25+=+81.25 ALIGN=MIDDLE  ALT=\"%28x-8.5%29%5E2+=+9+%2B+72.25+=+81.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "take the square root of both sides of this equation to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+8.5 ALIGN=MIDDLE  ALT=\"x+-+8.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = +/- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2881.25%29 ALIGN=MIDDLE  ALT=\"sqrt%2881.25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "add 8.5 go both sides of this equation to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+8.5 ALIGN=MIDDLE  ALT=\"x+=+8.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > +/- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2881.25%29 ALIGN=MIDDLE  ALT=\"sqrt%2881.25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = 17.51387819\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "x = -.513878189\r<BR>\n" );
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document.write( "they're the same answers you got using the quadratic formula.\r<BR>\n" );
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document.write( "you should remember the quadratic formula at least.\r<BR>\n" );
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document.write( "anytime you get a quadratic equation that you can't factor easily, use the quadratic formula.\r<BR>\n" );
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document.write( "if you prefer to use the completing the squares method, then remember that.\r<BR>\n" );
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document.write( "it's a little harder to explain how that works, but it's not too bad to work with once you know how.\r<BR>\n" );
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document.write( "you need to remember at least one of them.\r<BR>\n" );
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document.write( "the quadratic formula is a formula.  \r<BR>\n" );
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document.write( "the completing the square method is a method.\r<BR>\n" );
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document.write( "i believe the quadratic formula can be derived from the completing the squares method.\r<BR>\n" );
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document.write( "while the factoring method only works on quadratic equations when the factors are integers, the quadratic equation and the completing the squares method work on any quadratic equation.\r<BR>\n" );
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document.write( "even when the factoring method can be used, it's not always easy to spot the factors, especially when the a term (coefficient of the x^2 term) is not equal to 1.\r<BR>\n" );
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document.write( "bottom line is:\r<BR>\n" );
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document.write( "don't waste time trying to find the factors using the factoring method unless the question absolutely requires that you solve it that way.\r<BR>\n" );
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document.write( "as soon as you are having difficulty finding the factors, revert to the quadratic equation or the completing the squares method, whichever you feel more comfortable with.\r<BR>\n" );
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document.write( "here's some references for both the quadratic formula and the completing the squares method.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.purplemath.com/modules/sqrquad.htm\" target = \"_blank\">http://www.purplemath.com/modules/sqrquad.htm</a><BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://www.purplemath.com/modules/quadform.htm\" target = \"_blank\">http://www.purplemath.com/modules/quadform.htm</a><BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://www.jamesbrennan.org/algebra/quadratics/the_quadratic_formula.htm\" target = \"_blank\">http://www.jamesbrennan.org/algebra/quadratics/the_quadratic_formula.htm</a>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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