How can we do middle term splitting of x-10x-201?
You cant. Because the factors of 201 are not such. Use Sridhar Acharyas formula : x = (-b +- sqrt(b^2 - 4ac ))/ 2a Which comes directly from general quadratic eqn ax^2 + bx+ c by changing to x= So x = -(-10)+- sqrt(1004(1)(-201))/(2)(1) x = ( 10+-sqrt(904))/ 2 Hence you get two real roots using + and then -