document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=121030>Question 121030</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve by using the quadratic formula: 4x^2-6x=9. Express roots in EXACT radical form if necessary. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88808 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=88808\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To use the quadratic formula, the equation has to be in standard form, thus:\r<BR>\n" );
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document.write( "<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;\" >\r<BR>\n" );
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document.write( "Your equation:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-6x=9 ALIGN=MIDDLE  ALT=\"4x%5E2-6x=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > has to be re-arranged first.\r<BR>\n" );
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document.write( "Add -9 to both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-6x-9=0 ALIGN=MIDDLE  ALT=\"4x%5E2-6x-9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we have a = 4, b = -6, and c = -9 and we can put these values into the quadratic formula:\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%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%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=x+=+%28-%28-6%29+%2B-+sqrt%28+%28-6%29%5E2-4%2A4%2A%28-9%29+%29%29%2F%282%2A4%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-6%29+%2B-+sqrt%28+%28-6%29%5E2-4%2A4%2A%28-9%29+%29%29%2F%282%2A4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and simplify<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%286+%2B-+sqrt%28+36%2B144+%29%29%2F8+ ALIGN=MIDDLE  ALT=\"x+=+%286+%2B-+sqrt%28+36%2B144+%29%29%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%286+%2B-+sqrt%28+180+%29%29%2F8+ ALIGN=MIDDLE  ALT=\"x+=+%286+%2B-+sqrt%28+180+%29%29%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "160 = 2 * 2 * 3 * 3 * 5, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28180%29=6%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%28180%29=6%2Asqrt%285%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=x+=+%286+%2B-+6%2Asqrt%28+5+%29%29%2F8+ ALIGN=MIDDLE  ALT=\"x+=+%286+%2B-+6%2Asqrt%28+5+%29%29%2F8+\"   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=x+=+%283+%2B-+3%2Asqrt%28+5+%29%29%2F4+ ALIGN=MIDDLE  ALT=\"x+=+%283+%2B-+3%2Asqrt%28+5+%29%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%283%2B3sqrt%285%29%29%2F4 ALIGN=MIDDLE  ALT=\"x=%283%2B3sqrt%285%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%283-3sqrt%285%29%29%2F4 ALIGN=MIDDLE  ALT=\"x=%283-3sqrt%285%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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