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m^2 + m - 72 = 0----(1)
\n" ); document.write( "m^2 + [(9m) +(-8m)] - 72 = 0
\n" ); document.write( "[m^2+9m]-8m-72=0 (by additive associativity)
\n" ); document.write( "m(m+9)-8(m+9) = 0
\n" ); document.write( "mp -8p = 0 where p = (m+9)
\n" ); document.write( "p(m-8) = 0
\n" ); document.write( "(m+9)(m-8)=0
\n" ); document.write( "(m+9) = 0 gives m = -9
\n" ); document.write( "(m-8) = 0 gives m = 8
\n" ); document.write( "Answer: m = -9 and m = 8
\n" ); document.write( "Put m=-9 on the LHS of (1)and get 81-9-72 = 0 =RHS
\n" ); document.write( "m= 8 on the LHS of (1)and get 64+8-72 = 0 =RHS
\n" ); document.write( "Therefore our values m = -9 and m = 8 are correct\r
\n" ); document.write( "\n" ); document.write( "NOTE:
\n" ); document.write( "[The golden rule is: write the mid term as the sum of two terms whose product is the product of the square term and the constant term]
\n" ); document.write( "[HOW? Multiply the square term and the constant term: (m^2)X(-72) = -72m^2
\n" ); document.write( "And (-72) = -(1X2X2X2X3X3) = (9)X(-8) so that the mid term: (m) =[(9m) +(-8m)] and the product of these two parts:(9m) and (-8m) = -72m^2 using the concept
\n" ); document.write( "If the sign of the product is minus, and the middle term if +,then give the sign of the midterm to the larger set and the other sign to the smaller.
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