document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=603119>Question 603119</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve for x:<BR>\n" );
document.write( "x^2-6x+4=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #380616 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=380616\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2B4=0 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2B4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > by \"completing the square\" or you can apply the quadratic formula.<BR>\n" );
document.write( " <BR>\n" );
document.write( "COMPLETING THE SQUARE:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2B4=0 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2B4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x=-4 ALIGN=MIDDLE  ALT=\"x%5E2-6x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "At this point you would recognize that the left hand side of the equation resembles the square<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2=x%5E2-6x%2B9 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2=x%5E2-6x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, you add 9 to both sides of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x=-4 ALIGN=MIDDLE  ALT=\"x%5E2-6x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get the equivalent equation with the complete square on the left hand side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2B9=-4%2B9 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2B9=-4%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2B9=5 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2B9=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2=5 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "At this point, you know that either<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3=sqrt%285%29 ALIGN=MIDDLE  ALT=\"x-3=sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3=-sqrt%285%29 ALIGN=MIDDLE  ALT=\"x-3=-sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Adding 3 to both sides of the two equations above, you get the two solutions<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2Bsqrt%285%29 ALIGN=MIDDLE  ALT=\"x=3%2Bsqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3-sqrt%285%29 ALIGN=MIDDLE  ALT=\"x=3-sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "which can be summarized as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3+%2B-+sqrt%285%29 ALIGN=MIDDLE  ALT=\"x=3+%2B-+sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "THE QUADRATIC FORMULA<BR>\n" );
document.write( "All quadratic equations are of the form<BR>\n" );
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;\" > where a, b, and c are the coefficients which could be any number, with the only restriction that a cannot be zero.<BR>\n" );
document.write( "The solution is given by 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%5E2-4%2Aa%2Ac%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"x=%28-b+%2B-+sqrt%28b%5E2-4%2Aa%2Ac%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2B4=0 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2B4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "a=1, b=-6 and c=4, so the quadratic formula gives us<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%2A1%2A4%29%29%2F%282%2A1%29=%286+%2B-+sqrt%2836-16%29%29%2F2=%286+%2B-+sqrt%2820%29%29%2F2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That can be simplified like this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%286+%2B-+sqrt%2820%29%29%2F2=%286+%2B-+sqrt%284%2A5%29%29%2F2=%286+%2B-+sqrt%284%29%2Asqrt%285%29%29%2F2=%286+%2B-+2%2Asqrt%285%29%29%2F2=2%283+%2B-+sqrt%285%29%29%2F2=3+%2B-+sqrt%285%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );