document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=95514>Question 95514</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you help me on this one? I've been working on it for a while and can't figure it out.Thank You.\r<BR>\n" );
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document.write( "The square of a number added to the original number is 90.<BR>\n" );
document.write( "Determine all possible values of the number.\r<BR>\n" );
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document.write( "Larger Value:<BR>\n" );
document.write( "Smaller Value: </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #69504 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=69504\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Call the original unknown number x<BR>\n" );
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document.write( "Then the square of the original number is x^2<BR>\n" );
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document.write( "If you add the square of the number to the original number, the sum is 90. In equation form<BR>\n" );
document.write( "this is:<BR>\n" );
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document.write( "x^2 + x = 90<BR>\n" );
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document.write( "Subtract 90 from both sides of this equation so that the right side becomes zero. After this<BR>\n" );
document.write( "subtraction of 90 from both sides the equation becomes:<BR>\n" );
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document.write( "x^2 + x - 90 = 0<BR>\n" );
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document.write( "The left side of this equation can be factored to give:<BR>\n" );
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document.write( "(x + 10)(x - 9) = 0<BR>\n" );
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document.write( "(If you multiply the two factors on the left side, the product will be x^2 + x - 90.)<BR>\n" );
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document.write( "Notice now that this equation will be true if either of the two factors on the left side<BR>\n" );
document.write( "is equal to zero.  This is because zero times the other factor will be zero and that will<BR>\n" );
document.write( "equal the right side.<BR>\n" );
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document.write( "So the equation will be true if either x + 10 equals zero, or if x - 9 equals zero.<BR>\n" );
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document.write( "Solving these two equations will result in two values for x that will make quadratic<BR>\n" );
document.write( "equation true.<BR>\n" );
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document.write( "Solve x + 10 = 0 by subtracting 10 from both sides to get x = -10.  <BR>\n" );
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document.write( "Solve x - 9 = 0 by adding 9 to both sides to get x = +9<BR>\n" );
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document.write( "Therefore, the greater value of x is +9 and the lesser value is -10. (Greater value means<BR>\n" );
document.write( "that the number is further to the right on the number line. Since +9 is further to the<BR>\n" );
document.write( "right than -10, it is the greater value.)<BR>\n" );
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document.write( "Check by going back to the original problem.  If x is -10 then x^2 is +100 and the sum of<BR>\n" );
document.write( "these two is +90. That works.<BR>\n" );
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document.write( "Next if x is +9 then x^2 is +81 and the sum of these to is also +90. So the two answers work.<BR>\n" );
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document.write( "Hope this helps you to understand the problem and how to work it to get a solution.<BR>\n" );
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document.write( " </SPAN>\n" );
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