document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1006087>Question 1006087</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the cube of a number and twelve times the number is equal to 7 times the square of the number. Find the number </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #622233 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=622233\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = the number.\r<BR>\n" );
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document.write( "the cube of the number becomes x^3\r<BR>\n" );
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document.write( "12 times the number becomes 12x\r<BR>\n" );
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document.write( "7 time the square of the number becomes 7x^2\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "x^3 + 12x = 7x^2\r<BR>\n" );
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document.write( "subtract 7x^2 from both sides of the equation to get:\r<BR>\n" );
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document.write( "x^3 - 7x^2 + 12x = 0\r<BR>\n" );
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document.write( "factor out an x to get:\r<BR>\n" );
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document.write( "x * (x^2 - 7x + 12) = 0\r<BR>\n" );
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document.write( "factor the quadratic to get:\r<BR>\n" );
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document.write( "x * (x-4) * (x-3) = 0\r<BR>\n" );
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document.write( "set each of the factors equal to 0 and solve for x to get:\r<BR>\n" );
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document.write( "x = 0<BR>\n" );
document.write( "x = 4<BR>\n" );
document.write( "x = 3\r<BR>\n" );
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document.write( "those are the values of x that makes the original equation true.\r<BR>\n" );
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document.write( "the original equation is:\r<BR>\n" );
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document.write( "x^3 + 12x = 7x^2\r<BR>\n" );
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document.write( "when x = 0, you get 0 = 0 which is true.\r<BR>\n" );
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document.write( "when x = 3, you get 63 = 63 which is true.\r<BR>\n" );
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document.write( "when x = 4, you get 112 = 112 which is true.\r<BR>\n" );
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document.write( "you have 3 possible values of x that satisfy the constraints of the problem.\r<BR>\n" );
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document.write( "they are x = 0,3,4\r<BR>\n" );
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document.write( " </SPAN>\n" );
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