document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1023568>Question 1023568</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 9x^2-65x-56 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #639072 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=639072\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> start with 9x^2 - 65x - 56\r<BR>\n" );
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document.write( "since the middle term is negative and the constant term is negative, you are looking for factors that will subtract from each other to get -65.\r<BR>\n" );
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document.write( "in general, it works this way.\r<BR>\n" );
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document.write( "if the x term is negative and the constant term is positive, then you are looking for factors that will add up to the middle term and be negative.\r<BR>\n" );
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document.write( "if the x term is positive and the constant term is positive, then you are looking for factors that will add up to the middle term and be positive.\r<BR>\n" );
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document.write( "if the x term is negative and the constant term is negative, then you are looking for factors that will subtract from each other and be negative.\r<BR>\n" );
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document.write( "if the x term is positive and the constant term is negative, then you are looking for factors that will subtract from each other and be positive.\r<BR>\n" );
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document.write( "up to now you have accomplished the following:\r<BR>\n" );
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document.write( "you started with 9x^2 - 65x - 56.\r<BR>\n" );
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document.write( "set that equal to 0 to get 9x^2 - 65x - 56 = 0\r<BR>\n" );
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document.write( "the equation is now in standard form and can be factored manually, if that's possible.\r<BR>\n" );
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document.write( "i use the split the middle term method, which is similar to the box method.\r<BR>\n" );
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document.write( "both methods are superior to the guess and check method, unless the factors are obvious from inspection.\r<BR>\n" );
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document.write( "if the quadratic equation is not able to be factored manually, then you would need to resort to the quadratic formula.\r<BR>\n" );
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document.write( "the quadratic formula will factor any quadratic equation, whether that equation has real roots or complex roots.\r<BR>\n" );
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document.write( "back to your equation.\r<BR>\n" );
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document.write( "the equation is now 9x^2 - 65x - 56 = 0\r<BR>\n" );
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document.write( "you would first try to take out the greatest common factor.\r<BR>\n" );
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document.write( "it does not appear that this equation has a greatest common factor other than 1.\r<BR>\n" );
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document.write( "it is not divisible by 9 and it is not divisible by 3.\r<BR>\n" );
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document.write( "multiply the coefficient of the x^2 term by the constant term to get 9 * 56 = 504.\r<BR>\n" );
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document.write( "that's the number you are going to work with.\r<BR>\n" );
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document.write( "now you need to take factors of this until you find factors that subtract from each other to get 65.\r<BR>\n" );
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document.write( "start with 1 * 504<BR>\n" );
document.write( "next is 2 * 252<BR>\n" );
document.write( "next is 4 * 126<BR>\n" );
document.write( "next could be 8 * 63\r<BR>\n" );
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document.write( "you were looking for factors that are multiplied by each other to equal 504 and can be subtracted from each other to get 65.\r<BR>\n" );
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document.write( "1 * 504 had a difference too great.<BR>\n" );
document.write( "so did 2 * 252 and 4 * 126.\r<BR>\n" );
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document.write( "8 * 63 has a difference that is too small, because 63 - 8 = 55.\r<BR>\n" );
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document.write( "if there are factors that are integers that subtract from each other to get 65, they have to be between 4 * 126 and 8 * 63.\r<BR>\n" );
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document.write( "i started backtracking and went to a factor of 7.<BR>\n" );
document.write( "504 / 7 = 72.<BR>\n" );
document.write( "so i got:<BR>\n" );
document.write( "7 * 72 = 504<BR>\n" );
document.write( "when i subtracted 7 from 72, i got 65.<BR>\n" );
document.write( "that's the sect of factors i was looking for.\r<BR>\n" );
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document.write( "since the middle term is negative, then i need my factors to be + 7 and - 72.\r<BR>\n" );
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document.write( "here's where you split the middle term.\r<BR>\n" );
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document.write( "your equation is 9x^2 - 65x - 56 = 0\r<BR>\n" );
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document.write( "you split the middle term to get 9x^2 - 72x + 7x - 56 = 0\r<BR>\n" );
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document.write( "the middle term was - 65x and is now -72x + 7x which is equal to -65x once you add them together.\r<BR>\n" );
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document.write( "your equation is now 9x^2 - 72x + 7x - 56 = 0\r<BR>\n" );
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document.write( "you group the first two terms together and you group the last two terms together.\r<BR>\n" );
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document.write( "you get (9x^2 - 72x) + (7x - 56) = 0\r<BR>\n" );
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document.write( "you now want to factor the first set of terms and the second set of terms so that they'll both wind up with a common factor.\r<BR>\n" );
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document.write( "factor out a 9x from (9x^2 - 72x) to get 9x * (x - 8) = 0.\r<BR>\n" );
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document.write( "factor out a 7 from (7x - 56) to get 7 * (x - 8) = 0.\r<BR>\n" );
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document.write( "your equation now becomes 9x * (x - 8) + 7 * (x - 8) = 0.\r<BR>\n" );
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document.write( "your common factor is now (x - 8) which can be factored out.\r<BR>\n" );
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document.write( "your equation becomes:\r<BR>\n" );
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document.write( "(9x + 7) * (x - 8) = 0 after you factored out the common term of (x - 8).\r<BR>\n" );
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document.write( "these are the factors of your quadratic equation.\r<BR>\n" );
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document.write( "your solution is (9x + 7) * (x - 8) are factors of 9x^2 - 65x - 56.\r<BR>\n" );
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document.write( "if you need help in learning the various ways to factor a quadratic equation, try the following links.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.purplemath.com/modules/quadform.htm\" target = \"_blank\">http://www.purplemath.com/modules/quadform.htm</a>\r<BR>\n" );
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