document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=962445>Question 962445</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I could use some help with this literal equation. \r<BR>\n" );
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document.write( "Solve for T: n = aT^2-4T+m\r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #588048 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=588048\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> start with:\r<BR>\n" );
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document.write( "n = aT^2 - 4T + m\r<BR>\n" );
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document.write( "subtract m from both sides of the equation to get:\r<BR>\n" );
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document.write( "n - m = aT^2 - 4T\r<BR>\n" );
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document.write( "factor out the a on the right side of the equation to get:\r<BR>\n" );
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document.write( "n - m = a * (T^2 - 4/a * T)\r<BR>\n" );
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document.write( "in the preceding step you had to be a little creative because a * -4/a*T = -4*T\r<BR>\n" );
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document.write( "divide both sides of the equation by a to get:\r<BR>\n" );
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document.write( "(n-m)/a = T^2 - 4/a * T)\r<BR>\n" );
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document.write( "complete the squares on the right side of the equation to get:\r<BR>\n" );
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document.write( "(n-m)/a = (T-2/a)^2 - 4/a^2\r<BR>\n" );
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document.write( "add 4/a^2 to both sides of the equation to get:\r<BR>\n" );
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document.write( "(n-m)/a + 4/a^2 = (T-2/a)^2\r<BR>\n" );
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document.write( "take the square root of both sides of the equation to get:\r<BR>\n" );
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document.write( "sqrt((n-m)/a + 4/a^2) = T - 2/a\r<BR>\n" );
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document.write( "add 2/a to both sides of the equation to get:\r<BR>\n" );
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document.write( "sqrt((n-m)/a - 4/a^2) + 2/a = T\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "T = sqrt((n-m)/a + 4/a^2) + 2/a\r<BR>\n" );
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document.write( "the way to check is to give a random value to a and T and m and solve for n in the original equation.\r<BR>\n" );
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document.write( "then use that value of n and the values of a and m previously chosen to solve for T in the final equation.\r<BR>\n" );
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document.write( "I did and the solution is confirmed as good.\r<BR>\n" );
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document.write( "I used:\r<BR>\n" );
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document.write( "a = 9<BR>\n" );
document.write( "m = 5<BR>\n" );
document.write( "t = 2\r<BR>\n" );
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document.write( "i solved for n using the original equation to get n = 33.\r<BR>\n" );
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document.write( "i then used:\r<BR>\n" );
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document.write( "a = 9<BR>\n" );
document.write( "m = 5<BR>\n" );
document.write( "n = 33\r<BR>\n" );
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document.write( "i solved for t using the final equation to get t = 2.\r<BR>\n" );
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document.write( "that confirmed the solution is good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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