document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=102860>Question 102860</A>: <I><SPAN STYLE=\"word-break: break-all;\"> PLEASE HELP ME WITH THIS!!<BR>\n" );
document.write( "IF THE LENGTH OF THE SIDE OF A SQUARE IS INCREASED BY 6 UNITS, THE AREA IS MULTIPLIED BY 4. FIND THE ORIGINAL LENGTH. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #74817 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=74817\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you call the side of the original square x, then the area of the original square is x^2.<BR>\n" );
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document.write( "Now increase the length of each side by 6 units. So each side of the new square is x + 6.  <BR>\n" );
document.write( "This means that the area of this new square Bis (x + 6)^2 which multiplies out to x^2 + 12x + 36.<BR>\n" );
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document.write( "But the area new square is 4 times the area of the old square ... or 4x^2. So set the area<BR>\n" );
document.write( "of the new square equal to 4 times the area of the old square. In equation form this is<BR>\n" );
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document.write( "x^2 + 12x + 36 = 4x^2<BR>\n" );
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document.write( "To put this into a more standard form, subtract 4x^2 from both sides to get:<BR>\n" );
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document.write( "-3x^2 + 12x + 36 = 0<BR>\n" );
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document.write( "Note that -3 is a factor of all terms on the left side.  Therefore you can simplify <BR>\n" );
document.write( "this equation by dividing both sides (all terms) by -3 to reduce the equation to:<BR>\n" );
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document.write( "x^2 - 4x - 12 = 0<BR>\n" );
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document.write( "Factor the left side to get:<BR>\n" );
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document.write( "(x - 6)(x + 2) = 0<BR>\n" );
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document.write( "Notice this equation is true if either of the two factors on the left side equals zero.<BR>\n" );
document.write( "So set each factor equal to zero and solve for x. <BR>\n" );
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document.write( "x - 6 = 0 ... add 6 to both sides to get x = 6. This is one possible answer.<BR>\n" );
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document.write( "x + 2 = 0 ... subtract 2 from both sides to get x = -2 ... another possible answer.<BR>\n" );
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document.write( "But having a side of square equal to -2 doesn't make any sense. So the only reasonable answer<BR>\n" );
document.write( "is that x ... the side of the original square ... is 6.<BR>\n" );
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document.write( "Let's check the answer. If the sides of the original square are 6 units, then the area of<BR>\n" );
document.write( "the original square is 6 times 6 or 36 square units.<BR>\n" );
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document.write( "Increasing each side of the original square by 6 units makes the new square have sides of <BR>\n" );
document.write( "12 units. Therefore, the area of the new square is 12 times 12 or 144 square units.<BR>\n" );
document.write( "Notice that the area of the new square is 4 times the area of the original square ...<BR>\n" );
document.write( "4 times 36 equals 144 square units.<BR>\n" );
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document.write( "Hope this helps you to understand the problem.<BR>\n" );
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