document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1065334>Question 1065334</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve for the indicated letter.\r<BR>\n" );
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document.write( "R=vB^2+mB, for B\r<BR>\n" );
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document.write( "B=___ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #680482 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=680482\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> equation is:\r<BR>\n" );
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document.write( "R = vB^2 + mB\r<BR>\n" );
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document.write( "this is a quadratic equation that can be solved through use of the quadratic formula.\r<BR>\n" );
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document.write( "subtract R from both sides of the equation to get:\r<BR>\n" );
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document.write( "vB^2 + mB - R = 0\r<BR>\n" );
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document.write( "if you let:\r<BR>\n" );
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document.write( "x = B and:<BR>\n" );
document.write( "a = v and:<BR>\n" );
document.write( "b = m and:<BR>\n" );
document.write( "c = -R. then you get:\r<BR>\n" );
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document.write( "ax^2 + bx + c = 0\r<BR>\n" );
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document.write( "that's a quadratic equation in standard form.\r<BR>\n" );
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document.write( "the quadratic formula states that:\r<BR>\n" );
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document.write( "x = (-b + sqrt(b^2 - 4ac)) / (2a)\r<BR>\n" );
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document.write( "or:\r<BR>\n" );
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document.write( "x = (-b - sqrt(b^2 - 4ac)) /(2a)\r<BR>\n" );
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document.write( "all that's left to do is to replace back.\r<BR>\n" );
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document.write( "since x = B, then B must be equal to x.<BR>\n" );
document.write( "since a = v, then v must be equal to a.<BR>\n" );
document.write( "since b = m, then m must be equal to b.<BR>\n" );
document.write( "since c = -R then R must be equal to -c.\r<BR>\n" );
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document.write( "you will get:\r<BR>\n" );
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document.write( "x = (-b + sqrt(b^2 - 4ac)) / (2a) becomes:\r<BR>\n" );
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document.write( "B = (-m + sqrt(m^2 + 4vR)) / (2v)\r<BR>\n" );
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document.write( "and you will get:\r<BR>\n" );
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document.write( "x = (-b - sqrt(b^2 - 4ac)) /(2a) becomes:\r<BR>\n" );
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document.write( "B = (-m - sqrt(m^2 + 4vR)) / (2v)\r<BR>\n" );
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document.write( "your solution is that B = (-m + sqrt(m^2 + 4vR)) / (2v) or B = B = (-m - sqrt(m^2 + 4vR)) / (2v)\r<BR>\n" );
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document.write( "that should be it, if i did the translations correctly.\r<BR>\n" );
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document.write( "how can you check?\r<BR>\n" );
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document.write( "the way that i do it is to give values to the variables and then solve an equation that i know the solution to.  <BR>\n" );
document.write( "if i get the same answer than i assume i did it correctly.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "assume that B = -4 or B = 2.<BR>\n" );
document.write( "this means that B + 4 = 0 or B - 2 = 0.<BR>\n" );
document.write( "my factors would then be (B + 4) * (B - 2) = 0<BR>\n" );
document.write( "multiplying those factors together gets B^2 + 2B - 8 = 0<BR>\n" );
document.write( "adding 8 to both sides of the equation gets B^2 + 2B = 8<BR>\n" );
document.write( "multiplying both sides of the equation by 2 gets 2B^2 + 4B = 16<BR>\n" );
document.write( "flip the equation around to get 16 = 2B^2 + 4B.\r<BR>\n" );
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document.write( "16 = 2B^2 + 4B looks a lot like R = vB^2 + mB when:\r<BR>\n" );
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document.write( "R = 16<BR>\n" );
document.write( "v = 2<BR>\n" );
document.write( "m = 4\r<BR>\n" );
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document.write( "you want to solve for B using the equations we derived earlier.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "B = (-m + sqrt(m^2 + 4vR)) / (2v) or B = B = (-m - sqrt(m^2 + 4vR)) / (2v)\r<BR>\n" );
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document.write( "replacing m with 4 and v with 2 and R with 16, we get:\r<BR>\n" );
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document.write( "B = (-4 + sqrt(16 + 128)) / (4) or B = B = (-4 - sqrt(16 + 128)) / (4)\r<BR>\n" );
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document.write( "this makes B = 2 or B = -4\r<BR>\n" );
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document.write( "those are the values of B that we started from, so we can assume that the formulas are good.\r<BR>\n" );
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document.write( "this confirms that your solution is:\r<BR>\n" );
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document.write( "B = (-m + sqrt(m^2 + 4vR)) / (2v) or B = B = (-m - sqrt(m^2 + 4vR)) / (2v)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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