document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=23670>Question 23670</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I am really having a hard time analyzing this one, I hope someone could help me on this and I would really really appreciate it so much.\r<BR>\n" );
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document.write( "Question 1 : Explain a sequence of steps that can be used to solve any quadratic equation in the QUICKEST WAY.\r<BR>\n" );
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document.write( "Question 2 : Derive the quadratic formula used in solving quadratic equations.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #12437 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=12437\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) Determine whether or not the quadratic equation is factorable.<BR>\n" );
document.write( "If it is factorable, then factor it and apply the zero product principle to find the roots.<BR>\n" );
document.write( "If it is not factorable, or you are unable to determine its factorability, then use the quadratic formula to find the roots.\r<BR>\n" );
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document.write( "2) Derive the quadratic formula:\r<BR>\n" );
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document.write( "Start with the standard form of the general quadratic equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide through by a to get the x^2 coefficient = 1.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%28b%2Fa%29x+%2B+c%2Fa+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%28b%2Fa%29x+%2B+c%2Fa+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract c/a form both sides of the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%28b%2Fa%29x+=+-c%2Fa ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%28b%2Fa%29x+=+-c%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > Complete the square in the x-terms by adding the square of half the x-coefficient to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%28b%2Fa%29x+%2B+%28b%5E2%2F4a%5E2%29+=+%28b%5E2%2F4a%5E2%29-c%2Fa ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%28b%2Fa%29x+%2B+%28b%5E2%2F4a%5E2%29+=+%28b%5E2%2F4a%5E2%29-c%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the left side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+b%2F2a%29%5E2+=+%28b%5E2%2F4a%5E2%29-c%2Fa ALIGN=MIDDLE  ALT=\"%28x+%2B+b%2F2a%29%5E2+=+%28b%5E2%2F4a%5E2%29-c%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+b%2F2a+=+sqrt%28%28b%5E2%2F4a%5E2%29-c%2Fa%29 ALIGN=MIDDLE  ALT=\"x+%2B+b%2F2a+=+sqrt%28%28b%5E2%2F4a%5E2%29-c%2Fa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Note: There is (or should be) a + or - in front of the sqrt sign. Simplify the contents of the radical.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+b%2F2a+=+sqrt%28%28b%5E2+-+4ac%29%2F4a%5E2%29 ALIGN=MIDDLE  ALT=\"x+%2B+b%2F2a+=+sqrt%28%28b%5E2+-+4ac%29%2F4a%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of the denominator on the right side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+b%2F2a+=+%28sqrt%28b%5E2+-+4ac%29%29%2F2a ALIGN=MIDDLE  ALT=\"x+%2B+b%2F2a+=+%28sqrt%28b%5E2+-+4ac%29%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract b/2a from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b%2F2a%2B-sqrt%28b%5E2+-+4ac%29%2F2a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b%2F2a%2B-sqrt%28b%5E2+-+4ac%29%2F2a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the right side.<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%2F2a ALIGN=MIDDLE  ALT=\"x+=+%28-b%2B-sqrt%28b%5E2+-+4ac%29%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > And there you have it!<BR>\n" );
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