document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=274516>Question 274516</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you solve the equation: 0=3x-9&#8730;x-14? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #200317 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=200317\">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( "0=3x-9&#8730;x-14?\r<BR>\n" );
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document.write( "let k = sqrt(x)\r<BR>\n" );
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document.write( "equation becomes:\r<BR>\n" );
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document.write( "0 = 3k^2 - 9k - 14\r<BR>\n" );
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document.write( "this is a quadratic equation.\r<BR>\n" );
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document.write( "factor using the quadratic formula of k = <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( "a = 3<BR>\n" );
document.write( "b = -9<BR>\n" );
document.write( "c = -14<BR>\n" );
document.write( "2a = 6<BR>\n" );
document.write( "-b = 9<BR>\n" );
document.write( "b^2 = 81<BR>\n" );
document.write( "4ac = -168<BR>\n" );
document.write( "b^2 - 4ac = 81 + 168 = 249\r<BR>\n" );
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document.write( "quadratic formula becomes k = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289+%2B-+sqrt%28249%29%29%2F%286%29 ALIGN=MIDDLE  ALT=\"%289+%2B-+sqrt%28249%29%29%2F%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "k = (9 +/- 5.77973384)/6 which becomes:\r<BR>\n" );
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document.write( "k = 4.12995564<BR>\n" );
document.write( "k = -1.12995564\r<BR>\n" );
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document.write( "confirm these are correct by plugging into the equation of 3k^2 - 9k - 14 = 0.\r<BR>\n" );
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document.write( "once confirmed (done already), then you need to translate the k to x using the formula you used to derive k.\r<BR>\n" );
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document.write( "that formula was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+sqrt%28x%29 ALIGN=MIDDLE  ALT=\"k+=+sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "square both sides of this equation to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+k%5E2 ALIGN=MIDDLE  ALT=\"x+=+k%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "your answers of:\r<BR>\n" );
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document.write( "k = 4.12995564<BR>\n" );
document.write( "k = -1.12995564\r<BR>\n" );
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document.write( "become:\r<BR>\n" );
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document.write( "x = 17.05653359<BR>\n" );
document.write( "x = 1.276799748\r<BR>\n" );
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document.write( "plug these into the original equation of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+-9%2Asqrt%28x%29+-+14+=+0 ALIGN=MIDDLE  ALT=\"3x+-9%2Asqrt%28x%29+-+14+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > to confirm they are good.\r<BR>\n" );
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document.write( "the value of 17.05653359 is confirmed as good since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2817.05653359%29 ALIGN=MIDDLE  ALT=\"sqrt%2817.05653359%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = +/- 4.12995564 except that you have to use the positive square root only.\r<BR>\n" );
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document.write( "the value of 1.276799748 is confirmed as good since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281.276799748%29 ALIGN=MIDDLE  ALT=\"sqrt%281.276799748%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = +/- 1.12995564 except that you have to use the negative square root only.<BR>\n" );
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