Solve v_{0}=p^2+1+p^2-4p+13

$$v _ { 0 } = p ^ { 2 } + 1 + p ^ { 2 } - 4 p + 13$$

Solve for v_0

$$v_{0}=2\left(p^{2}-2p+7\right)$$

Solution Steps

Combine p^{2} and p^{2} to get 2p^{2}.

$$v_{0}=2p^{2}+1-4p+13$$

Add 1 and 13 to get 14.

$$v_{0}=2p^{2}+14-4p$$

Solve for p (complex solution)

$$p=\frac{\sqrt{2v_{0}-24}}{2}+1$$

$$p=-\frac{\sqrt{2v_{0}-24}}{2}+1$$

Solve for p

$$p=\frac{\sqrt{2v_{0}-24}}{2}+1$$

$$p=-\frac{\sqrt{2v_{0}-24}}{2}+1\text{, }v_{0}\geq 12$$