Solve n50=n[2+(n-1)1]

$$n 50 = n [ 2 + ( n - 1 ) 1 ]$$

Solve for n_50

$$n_{50}=n\left(n+1\right)$$

Solution Steps

Use the distributive property to multiply n-1 by 1.

$$n_{50}=n\left(2+n-1\right)$$

Subtract 1 from 2 to get 1.

$$n_{50}=n\left(1+n\right)$$

Use the distributive property to multiply n by 1+n.

$$n_{50}=n+n^{2}$$

Solve for n

$$n=\frac{-\sqrt{4n_{50}+1}-1}{2}$$

$$n=\frac{\sqrt{4n_{50}+1}-1}{2}\text{, }n_{50}\geq -\frac{1}{4}$$