document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=328707>Question 328707</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could I please get help with this problem. I have tried different ways to solve it and can not get it to come out. In the book it shows to use -1 in front. -1(30w²+w+1.  Don't really understand.Do I need to change signs before factoring? Factor completely and check. Thank you for your time.\r<BR>\n" );
document.write( "\n" );
document.write( "-30w² + w + 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #235508 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=235508\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation is -30w^2 + w + 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The reason they tell you to use a -1 in front of it is because it's easier to factor when the coefficient of the x^2 term is positive.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This can be done in the following manner.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Set your equation = to 0 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-30w^2 + w + 1 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Multiply both sides of this equation by -1 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "30w^2 - w - 1 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The right sides of the equation remains the same because 0 * anything is still 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The left side of the equation now has a positive coefficient for the x^2 term.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You still have a problem with this equation because the coefficient of the x^2 term is not equal to 1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Making the coefficient of the x^2 = 1 sometimes helps in factoring and is necessary if solving using the completing the squares method.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you factor out the 30 from the left hand side of this equation, you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "30 * (x^2 - (1/30)*x - (1/30)) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you can factor (x^2 - (1/30)*x - (1/30)) then you should be home free.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You can factor this using the quadratic equation or by completing the squares if you can't eyeball the solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since 1/30 is the same as (1/5) * (1/6), it's possible that our solution will be a combination of these.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Your factors are (x - (1/5)) * (x + (1/6)) = 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I'm cheating now because I already know the solution.  I was not able to eyeball the solution without first using the quadratic formula to solve for x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Regardless, if these factors are good, then you should be able to substitute in the original equation to confirm that the equation is true with them.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since the factors are (x - (1/5)) * (x + (1/6)) = 0, then:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = (1/5) or x = (-1/6)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Substitute (1/5) in the original equation first.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The original equation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-30x^2 + x + 1 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "When x = (1/5), this equation becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-30 * (1/25) + (1/5) + 1 = 0 which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-30/25 + 1/5 + 1 = 0 which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-30/25 + 5/25 + 25/25 = 0 which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-25/25 + 25/25 = 0 which is true confirming the value of x = (1/5) is good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "When x = - (1/6), this equation becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-30/36 - 1/6 + 1 = 0 which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-30/36 - 6/36 + 36/36 = 0 which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-36/36 + 36/36 = 0 which is true confirming the value of x = - (1/6) is also good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Those are your solutions.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Your original expression was:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-30x^2 + x + 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You set it equal to 0 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-30x^2 + x + 1 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you factored out the (-30) to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(-30) * (x^2 - x/30 - 1/30) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You factored x^2 - x/30 - 1/30 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(-30) * (x - (1/5)) * (x + (1/6)) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Those are your factors.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you multiply these factors together, you should get your original equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-30 * (x - 1/5) = -30x + 6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(-30x + 6) * (x + 1/6) = -30x^2 -5x + 6x + 1 which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-30x^2 + x + 1 which is where you started from.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );