document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1044324>Question 1044324</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I am preparing for a test and I would like to know how to solve problems using a quadratic equation. For example : \"The length of a book is 4 cm more than its width and the area of the face of the book is 320 cm^2. Find the dimensions of the face of the book.\"  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #659598 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=659598\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the first thing you have to do is to translate the problem into an algebraic equation.\r<BR>\n" );
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document.write( "if it is linear, you then solve the linear equation.\r<BR>\n" );
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document.write( "if it is quadratic, you then solve the quadratic equation.\r<BR>\n" );
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document.write( "a quadratic equation is an equation in which the highest exponent of any term is equal to 2.\r<BR>\n" );
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document.write( "your problem states:\r<BR>\n" );
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document.write( "The length of a book is 4 cm more than its width and the area of the face of the book is 320 cm^2. \r<BR>\n" );
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document.write( "you should know that length * width = area.\r<BR>\n" );
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document.write( "you are given that the length of the book is 4 cm more than its width.\r<BR>\n" );
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document.write( "you need to translate this to an algebraic expression.\r<BR>\n" );
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document.write( "let x equal the length.\r<BR>\n" );
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document.write( "since the with is equal to 4 cm more than the length, you get:\r<BR>\n" );
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document.write( "length = x\r<BR>\n" );
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document.write( "width = x + 4.\r<BR>\n" );
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document.write( "since length * width = area, you get:\r<BR>\n" );
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document.write( "x * (x + 4) =area\r<BR>\n" );
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document.write( "since area = 320 cm^2, you get:\r<BR>\n" );
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document.write( "x * (x + 4) = 320\r<BR>\n" );
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document.write( "you don't always show the unis involved (like cm and cm^2), but they're implied and they have to be consistent with each other.\r<BR>\n" );
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document.write( "now that you have your equation, you need to simplify it so you can solve it.\r<BR>\n" );
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document.write( "simplify by applying the distributive law to get:\r<BR>\n" );
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document.write( "x^2 + 4x = 320\r<BR>\n" );
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document.write( "subtract 320 from both side of the equation to get:\r<BR>\n" );
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document.write( "x^2 + 4x - 320 = 0\r<BR>\n" );
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document.write( "the equation is now in standard form of a quadratic equation and can be factored using one of various method.\r<BR>\n" );
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document.write( "factor the equation to get (x + 20) * (x - 16) = 0\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = -20 or x = 16.\r<BR>\n" );
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document.write( "x can't be negative, so x = 16 is your answer.\r<BR>\n" );
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document.write( "the length is equal to x which is equal to 16 centimeters..\r<BR>\n" );
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document.write( "the width is equal to x + 4 which is equal to 20 centimeters.\r<BR>\n" );
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document.write( "length times width = 16 * 20 = 320 square centimeters.\r<BR>\n" );
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document.write( "there are various methods to factor a quadratic equation.\r<BR>\n" );
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document.write( "here are some lessons that show you how to do them.\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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document.write( "<a  rel=nofollow HREF= \"http://www.regentsprep.org/regents/math/algtrig/atv1/revfactorgrouping.htm\" target = \"_blank\">http://www.regentsprep.org/regents/math/algtrig/atv1/revfactorgrouping.htm</a>\r<BR>\n" );
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document.write( "there are even more methods, such as the indian method, that are not commonly used.\r<BR>\n" );
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document.write( "i used the factor by grouping method most of the time.\r<BR>\n" );
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document.write( "if you get stuck and can't factor the quadratic by any other means, then use the quadratic formula.\r<BR>\n" );
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document.write( "but first you need to get it into standard form.\r<BR>\n" );
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document.write( "the standard form of a quadratic equation is ax^2 + bx + c = 0\r<BR>\n" );
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document.write( "a is equal to the coefficient of the x^2 term.<BR>\n" );
document.write( "b is equal to the coefficient of the x term.<BR>\n" );
document.write( "c is equal to the constant term.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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