document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=496643>Question 496643</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The square of the differene between a number and 12 is twice the number.<BR>\n" );
document.write( "what is 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 #336519 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=336519\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x be the unknown number. Then the difference between the unknown number and 12 can be written as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+12 ALIGN=MIDDLE  ALT=\"x+-+12\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This quantity is to be squared and it is to equal two times the unknown number. In equation form this becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-12%29%5E2+=+2x ALIGN=MIDDLE  ALT=\"%28x-12%29%5E2+=+2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Squaring out the left side makes the equation become:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+24x+%2B+144+=+2x ALIGN=MIDDLE  ALT=\"x%5E2+-+24x+%2B+144+=+2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Subtract 2x from both sides to get the equation into the more conventional quadratic form having zero on the right side:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+26x+%2B+144+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+26x+%2B+144+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "This quadratic equation can be solved by factoring the left side as follows:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+18%29%2A%28x+-+8%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+-+18%29%2A%28x+-+8%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "And this equation will be true if either of the factors is zero because a multiplication on the left side by a zero factor makes the left side equal to the right side. So either:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+18+=+0+ ALIGN=MIDDLE  ALT=\"x+-+18+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > which by adding 18 to both sides becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+18 ALIGN=MIDDLE  ALT=\"x+=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "or:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+8+=+0 ALIGN=MIDDLE  ALT=\"x+-+8+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > which by adding 8 to both sides becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+8 ALIGN=MIDDLE  ALT=\"x+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "If you didn't recognize the factoring, you could always use the quadratic formula to solve the quadratic equation. Recognize that the quadratic equation that we developed is in the form:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "and by comparing this form to the equation we developed, you can see that a = 1, b = -26, and c = 144. Substitute these values into the quadratic formula as follows:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-26%29+%2B-+sqrt%28+%28-26%29%5E2-4%2A1%2A144+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-26%29+%2B-+sqrt%28+%28-26%29%5E2-4%2A1%2A144+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Within the radical sign, square the -26 and multiply out the -4*1*144 to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-26%29+%2B-+sqrt%28+676-576+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-26%29+%2B-+sqrt%28+676-576+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "and the terms in the radical become 100. Taking the square root of the 100 reduces the formula to:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-26%29+%2B-+10%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-26%29+%2B-+10%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Remove the parentheses around the -26 and also multiply out the denominator to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2826+%2B-+10%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%2826+%2B-+10%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "and this becomes either <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2826%2B10%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%2826%2B10%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2826-10%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%2826-10%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and from these we again get the answers:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+18 ALIGN=MIDDLE  ALT=\"x+=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+8 ALIGN=MIDDLE  ALT=\"x+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( ".<BR>\n" );
document.write( "Check: Does <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2818+-+12%29%5E2 ALIGN=MIDDLE  ALT=\"%2818+-+12%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > equal <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A18 ALIGN=MIDDLE  ALT=\"2%2A18\"   DISABLED_style= \"max-width:90%; height:auto;\" >? If you work this out you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36+=+36 ALIGN=MIDDLE  ALT=\"36+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" > so it does work.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Also check: Does <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%288+-+12%29%5E2+ ALIGN=MIDDLE  ALT=\"+%288+-+12%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > equal <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A8 ALIGN=MIDDLE  ALT=\"2%2A8\"   DISABLED_style= \"max-width:90%; height:auto;\" >? If you work this out you find that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%29%5E2+=+16 ALIGN=MIDDLE  ALT=\"%28-4%29%5E2+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" > are equal and so this solution also works.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The two answers to this problem that will satisfy the requirements are x = 18 and x = 8.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you understand how to go about working this problem. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );