Question

Solve: $1-3m+\frac{9m(m-1)}{2}=559$

Answer 1

$1-3m+\frac{9m(m-1)}{2}=559$

$\frac{2-6m+9m^2-9m}{2}=559$

$9m^2-15m+2=1118$

$\Rightarrow 9m^2-15m-1116=0$

$\Rightarrow 3(3m^2-5m-372)=0$

$\Rightarrow 3m^2-36m+31m-372=0$

$\Rightarrow 3m(m-12)+31(m-12)=0$

$\Rightarrow (m-12)(3m+31)=0$

$\Rightarrow m=12\text{or}-\frac{31}{3}$

Hence the value of $m$ are $12$ and $-\frac{31}{3}$.