document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=449383>Question 449383</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hey, Im in much need of help to figure out how to factor/solve qudaratic equations that are not in X^2+bx+c=0 form. for example,how do you factor 4x^2=4x+5? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #309135 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=309135\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> how do you factor 4x^2=4x+5?<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Rearrange:<BR>\n" );
document.write( "4x^2 - 4x - 5 = 0<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Using the quadratic formula:<BR>\n" );
document.write( "x = [4 +- sqrt(16-4*4*-5)]/(2*4)<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "x = [4 +- sqrt(96)]/8<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "x = [4 +- 4sqrt(6)]/8<BR>\n" );
document.write( "----<BR>\n" );
document.write( "r1 = (1/2)+(1/2)sqrt(6) or r2 = (1/2)-(1/2)sqrt(6)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Each of these is a root of the quadratic.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "The factored form would be (x-r1)(x-r2) = 0<BR>\n" );
document.write( "===============================================<BR>\n" );
document.write( "So the quadratic formula can ALWAYS be used to factor<BR>\n" );
document.write( "a quadratic polynomial.<BR>\n" );
document.write( "===============================================<BR>\n" );
document.write( "If you are familiar with FOIL, Inverse FOIL can<BR>\n" );
document.write( "be used to factor some quadratics.<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Example:<BR>\n" );
document.write( " 2x^2+7x-15 = 0<BR>\n" );
document.write( "ac = 2*-15 = -30<BR>\n" );
document.write( "b = 7<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Think of 2 numbers whose product is ac and whose sum is b:<BR>\n" );
document.write( "ac = 10*-3 = -30<BR>\n" );
document.write( "b = 10+ -3 = 7<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Rewrite the quadratic replacing the \"b-term\":<BR>\n" );
document.write( "2x^2 + 10x-3x -15 = 0<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Factor the 1st two and the last two terms separately:<BR>\n" );
document.write( "2x(x+5)-3(x+5) = 0<BR>\n" );
document.write( "Factor again:<BR>\n" );
document.write( "(x+5)(2x-3) = 0<BR>\n" );
document.write( "=============================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "=============================<BR>\n" );
document.write( "  </SPAN>\n" );
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