document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=122820>Question 122820</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the square of 3 more than a number is 9, 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 #90165 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=90165\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x be the unknown number.<BR>\n" );
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document.write( "Then 3 more than this unknown number is x + 3<BR>\n" );
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document.write( "And squaring this quantity is:<BR>\n" );
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document.write( "(x + 3)^2<BR>\n" );
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document.write( "The problem tells you that this is to equal 9. In equation form this is:<BR>\n" );
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document.write( "(x + 3)^2 = 9<BR>\n" );
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document.write( "Squaring out the left side results in this equation becoming:<BR>\n" );
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document.write( "x^2 + 6 x + 9 = 9<BR>\n" );
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document.write( "Subtract 9 from both sides results in:<BR>\n" );
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document.write( "x^2 + 6x = 0<BR>\n" );
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document.write( "Factor the left side:<BR>\n" );
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document.write( "x(x + 6) = 0<BR>\n" );
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document.write( "Note that the left side of the equation will be zero if either of the two factors is<BR>\n" );
document.write( "equal to zero ... because multiplying by a zero factor will result in an answer of zero.<BR>\n" );
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document.write( "So for the two answers, either:<BR>\n" );
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document.write( "x = 0<BR>\n" );
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document.write( "or<BR>\n" );
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document.write( "x + 6 = 0<BR>\n" );
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document.write( "In this second case, subtracting 6 from both sides results in:<BR>\n" );
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document.write( "x = -6<BR>\n" );
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document.write( "So the two answers are x = 0 and x = -6.<BR>\n" );
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document.write( "To check these two answers, return to the equation:<BR>\n" );
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document.write( "(x + 3)^2 = 9<BR>\n" );
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document.write( "Try the first answer we got ... x = 0. Substituting this value of x into the equation<BR>\n" );
document.write( "and you get:<BR>\n" );
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document.write( "(0 + 3)^2 = 9<BR>\n" );
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document.write( "This simplifies to 3^2 = 9 and that, of course, checks out.<BR>\n" );
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document.write( "Next in the equation substitute -6 for x and you get:<BR>\n" );
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document.write( "(-6 + 3)^2 = 9<BR>\n" );
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document.write( "Combining the two numbers in the parentheses leads to:<BR>\n" );
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document.write( "(-3)^2 = 9<BR>\n" );
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document.write( "And this too is correct because squaring -3 results in +9. <BR>\n" );
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document.write( "So our answers of x = 0 and x = -6 are correct.<BR>\n" );
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document.write( "Hope this helps you to understand the problem and how to work out an answer.<BR>\n" );
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document.write( " </SPAN>\n" );
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