document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=63920>Question 63920</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321279220/algebrahomeworkh>introductory and intermediate algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> m^2-8m+15=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #44569 by </B><A HREF=/tutors/aboutme.mpl?userid=praseenakos@yahoo.com><B>praseenakos@yahoo.com(507)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=praseenakos@yahoo.com><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=praseenakos@yahoo.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=44569\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ANSWER:\r<BR>\n" );
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document.write( "m^2-8m+15=0\r<BR>\n" );
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document.write( "ANSWER;\r<BR>\n" );
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document.write( "This is a quadratic equation in the variable,' m'\r<BR>\n" );
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document.write( "WE CAN SOLVE THIS PROBLEM USING DIFFERENT METHODS.\r<BR>\n" );
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document.write( "1. SPLITTING MIDDLE TERMS\r<BR>\n" );
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document.write( "2. USING QUADRATIC FORMULA\r<BR>\n" );
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document.write( "Lets take the first method,\r<BR>\n" );
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document.write( "m^2-8m+15=0, here we have coefficent of m is -8 and the consant term is  +15\r<BR>\n" );
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document.write( "Find out two numbers so that their product(multiplication) is +15 and their sum is -8\r<BR>\n" );
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document.write( "such two numbers are -3 and -5\r<BR>\n" );
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document.write( "because -3* -5 = +15  and -3 + -5 = -8\r<BR>\n" );
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document.write( "Now split the middle term  as follows,\r<BR>\n" );
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document.write( "m^2 - 5m - 3m + 15 = 0\r<BR>\n" );
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document.write( "Now group the terms as follows,\r<BR>\n" );
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document.write( "(m^2 - 5m )- (3m - 15) = 0\r<BR>\n" );
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document.write( "Take out common terms from each group,\r<BR>\n" );
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document.write( "m ( m - 5 ) - 3 ( m - 5 ) = 0\r<BR>\n" );
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document.write( "again (m-5) is common in both the groups, so take them out,\r<BR>\n" );
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document.write( "(m-5)(m -3) = 0\r<BR>\n" );
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document.write( "This implies, either (m-5) is equal to 0 or (m -3) = 0\r<BR>\n" );
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document.write( "If  (m-5) = o   \r<BR>\n" );
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document.write( "==> m = 5 and   \r<BR>\n" );
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document.write( "If(m -3) =0 ==> m = 3\r<BR>\n" );
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document.write( "Thos we got two values for m.\r<BR>\n" );
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document.write( "Whichj is the required solutions for the given equation.\r<BR>\n" );
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document.write( "Now lets take the second method,\r<BR>\n" );
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document.write( "We have the   quadratic formula, \r<BR>\n" );
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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;\" >   for solving a standard quadratic equation, ax^2 + bx + c = 0\r<BR>\n" );
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document.write( "Compare this with our given equation,\r<BR>\n" );
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document.write( "then we have ,\r<BR>\n" );
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document.write( "a= 1, b = -8 and c= 15\r<BR>\n" );
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document.write( "substitute these values in the quadratic formula,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"m+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-%28-8%29%2B-+sqrt%28+%28-8%29%5E2-4%2A1%2A15%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"m+=+%28-%28-8%29%2B-+sqrt%28+%28-8%29%5E2-4%2A1%2A15%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%288+%2B-+sqrt%28+64-60+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"m+=+%288+%2B-+sqrt%28+64-60+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%288+%2B-+sqrt%28+4%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"m+=+%288+%2B-+sqrt%28+4%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%288+%2B-+2%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"m+=+%288+%2B-+2%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "That means m = (8 + 2)/(2)  or m = (8 - 2)/(2)\r<BR>\n" );
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document.write( "==>  m = 10/2  or  m = 6/2\r<BR>\n" );
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document.write( "==>  m = 5   or m = 3\r<BR>\n" );
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document.write( "Here also we got the same value.\r<BR>\n" );
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document.write( "You can use any method  which you find easier.\r<BR>\n" );
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document.write( "Hope you understood.\r<BR>\n" );
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document.write( "Regards.\r<BR>\n" );
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document.write( "praseenakos@yahoo.com\r<BR>\n" );
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document.write( " </SPAN>\n" );
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