document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1027956>Question 1027956</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write a quadratic equation and solve\r<BR>\n" );
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document.write( "The difference of two numbers is 6 and the difference of their squares is 60. Find the numbers </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #643133 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=643133\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let a be the larger number.<BR>\n" );
document.write( "let b be the smaller number.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "a - b = 6<BR>\n" );
document.write( "a^2 - b^2 = 60\r<BR>\n" );
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document.write( "in the first equation, solve for a to get a = b + 6\r<BR>\n" );
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document.write( "in the second equation, replace a with (b+6) to get:\r<BR>\n" );
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document.write( "(b+6)^2 - b^2 = 60\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "b^2 + 12b + 36 - b^2 = 60\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "12b + 36 = 60\r<BR>\n" );
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document.write( "subtract 36 from both sides of this equation to get:\r<BR>\n" );
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document.write( "12b = 24\r<BR>\n" );
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document.write( "solve for b to get:\r<BR>\n" );
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document.write( "b = 2\r<BR>\n" );
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document.write( "if b = 2, the a - b = 6 becomes a - 2 = 6\r<BR>\n" );
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document.write( "add 2 to both sides of this equation to get a = 8\r<BR>\n" );
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document.write( "when a = 8 and b = 2, you get:\r<BR>\n" );
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document.write( "a - b = 8 - 2 = 6<BR>\n" );
document.write( "a^2 - b^2 = 8^2 - 2^2 = 64 - 4 = 60\r<BR>\n" );
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document.write( "this confirms the solution is correct.\r<BR>\n" );
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document.write( "the numbers are 8 and 2.\r<BR>\n" );
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document.write( "subtract the smaller number from the larger number and you get 6.\r<BR>\n" );
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document.write( "subtract the square of the smaller number from the square of the larger number and you get 60.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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