13m² + 3m = 0
m² + ( 3m / 13 ) = 0
m² + ( 3m / 13 ) + ( 3² / 26² ) = ( 3² / 26² )
m² + ( 3m / 13 ) + ( 9 / 676 ) = ( 9 / 676 )
( m + ( 3 / 26) )² = ( 9 / 676 )
m + ( 3 / 26 ) = ±( 3 / 26 )
m = ( -3 / 26 ) ± ( 3 / 26 )
13m^2 +3m = 0
DIVIDE BY 13
m^2 + 3m/13 = 0
ADD 9/ 676
m^2 + 3m/13 + 9/676 = 9/676
( m + 3/26)^2 = 9/676
m = 3/26 - 3/26 OR -3/26 -3/26
m = 0 OR -6/26
m = 0 OR -3/13 ANSWER
13m^2 + 3m = 0
m^2 + 3/13(m) = 0
m^2 + 3/26(m) + 9/676 = 9/676
(m + 3/26)^2 = 9/676
m + 3/26 = ±√(9/676)
m = 3/26 ± 3/26
m = 0
m = -6/26...which reduces to - 3/13
reference
http://patrickjmt.com/quadratic-equations-completi...
m² + (3 /13 )m +_____ = 0===> take (1/2) the coefficient of the second term and square it. [(1/2)(3/13)]² =(3/26)² = 9 / 676
m² + (3/26))m + 9/676 = 9/767 ===> if we add 9/676 to the left side we must add 9/676 to the right side.
(m + 3/26)² - 9/676 =0
13 [ m² + (3/13) m ] = 0
m² + (3/13) m + 9/676 = 9/676
[ m + 3/26 ]² = 9/676
[ m + 3/26 ] = ± 3/26
m = - 3/26 ± 3/26
m = 0 , - 3/13
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Verified answer
13m² + 3m = 0
m² + ( 3m / 13 ) = 0
m² + ( 3m / 13 ) + ( 3² / 26² ) = ( 3² / 26² )
m² + ( 3m / 13 ) + ( 9 / 676 ) = ( 9 / 676 )
( m + ( 3 / 26) )² = ( 9 / 676 )
m + ( 3 / 26 ) = ±( 3 / 26 )
m = ( -3 / 26 ) ± ( 3 / 26 )
13m^2 +3m = 0
DIVIDE BY 13
m^2 + 3m/13 = 0
ADD 9/ 676
m^2 + 3m/13 + 9/676 = 9/676
( m + 3/26)^2 = 9/676
m = 3/26 - 3/26 OR -3/26 -3/26
m = 0 OR -6/26
m = 0 OR -3/13 ANSWER
13m^2 + 3m = 0
m^2 + 3/13(m) = 0
m^2 + 3/26(m) + 9/676 = 9/676
(m + 3/26)^2 = 9/676
m + 3/26 = ±√(9/676)
m = 3/26 ± 3/26
m = 0
m = -6/26...which reduces to - 3/13
reference
http://patrickjmt.com/quadratic-equations-completi...
13m² + 3m = 0
m² + (3 /13 )m +_____ = 0===> take (1/2) the coefficient of the second term and square it. [(1/2)(3/13)]² =(3/26)² = 9 / 676
m² + (3/26))m + 9/676 = 9/767 ===> if we add 9/676 to the left side we must add 9/676 to the right side.
(m + 3/26)² - 9/676 =0
13 [ m² + (3/13) m ] = 0
m² + (3/13) m + 9/676 = 9/676
[ m + 3/26 ]² = 9/676
[ m + 3/26 ] = ± 3/26
m = - 3/26 ± 3/26
m = 0 , - 3/13