document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=916822>Question 916822</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I really need help understanding this ;/\r<BR>\n" );
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document.write( " What are the zero(s) of the function f(x) = the quantity of 5 x squared minus 25 x, all over x?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #556311 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=556311\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> equation is y = (5x^2 + x)/x<BR>\n" );
document.write( "set y = 0 to get:<BR>\n" );
document.write( "(5x^2 + x)/x = 0<BR>\n" );
document.write( "multiply both sides of the equation by x to get:<BR>\n" );
document.write( "5x^2 + x = 0<BR>\n" );
document.write( "this is a quadratic equation that you can factor using any of the methods that work.<BR>\n" );
document.write( "i'll use the quadratic formula.<BR>\n" );
document.write( "since the eqaution is in standard form of ax^2 + bx + c = 0, you can get the values of a, b, and c as follows:<BR>\n" );
document.write( "a = 5<BR>\n" );
document.write( "b = 1<BR>\n" );
document.write( "c = 0<BR>\n" );
document.write( "the quadratic formula is x = (-b +/- sqrt(b^2-4ac))/(2a)<BR>\n" );
document.write( "replace a with 5 and b with 1 and c with 0 and you will get:<BR>\n" );
document.write( "x = 0 or x = -1/5<BR>\n" );
document.write( "those are your possible solutions.<BR>\n" );
document.write( "you have to confirm that they are good by replacing x with them in the original equation to see if the equation is true.<BR>\n" );
document.write( "always confirm using the original equation or expression.<BR>\n" );
document.write( "the original equation is (5x^2 + x)/x = 0<BR>\n" );
document.write( "when x = 0, the original equation of (5x^2 + x)/x = 0 becomes (0/0) = 0 which becomes undefined = 0 which is not true.<BR>\n" );
document.write( "the expression 0/0 is undefined because the denominator is equal to 0.<BR>\n" );
document.write( "x = 0 is therefore not a solution to this problem.<BR>\n" );
document.write( "when x = -1/5, the original equation of (5x^2 + x)/x = 0 becomes (5*(1/25 - 1/5) / (1/5) = 0 which becomes (1/5 - 1/5) / (1/5) = 0 which becomes 0 / (1/5) = 0 which becomes 0 = 0 which is true.<BR>\n" );
document.write( "x = -1/5 is therefore the only solution to this problem.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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