x^2 - 4x - 45 = 0
by using the ' splitting the middle term method ' ,
_ x _ = - 45
_ + _ = - 4
the blanks ca be filled by using the digits ' -9 and 5 '
as -9 x 5 = - 45
and -9 + 5 = - 4
therefore ,
x^2 - 9 x + 4x - 45 = 0
taking the common factor out ,
x ( x-9 ) + 4 ( x - 9 ) = 0
therefore ,
a ) x - 9 = 0
and x = 9
b ) x + 4 =0
and x = -4