Solve 2x^2-5x+p^2+q^2=0

$$2 x ^ { 2 } - 5 x + p ^ { 2 } + q ^ { 2 } = 0$$

Solve for p (complex solution)

$$p=-\sqrt{-2x^{2}+5x-q^{2}}$$

$$p=\sqrt{-2x^{2}+5x-q^{2}}$$

Solve for q (complex solution)

$$q=-\sqrt{-2x^{2}+5x-p^{2}}$$

$$q=\sqrt{-2x^{2}+5x-p^{2}}$$

Solve for p

$$p=\sqrt{-2x^{2}+5x-q^{2}}$$

$$p=-\sqrt{-2x^{2}+5x-q^{2}}\text{, }\left(q>-\frac{5\sqrt{2}}{4}\text{ and }x\leq \frac{\sqrt{25-8q^{2}}+5}{4}\text{ and }x\geq \frac{-\sqrt{25-8q^{2}}+5}{4}\text{ and }|q|<\frac{5\sqrt{2}}{4}\right)\text{ or }\left(x=\frac{5}{4}\text{ and }|q|\leq \frac{5\sqrt{2}}{4}\right)$$

Solve for q

$$q=\sqrt{-2x^{2}+5x-p^{2}}$$

$$q=-\sqrt{-2x^{2}+5x-p^{2}}\text{, }\left(p>-\frac{5\sqrt{2}}{4}\text{ and }x\leq \frac{\sqrt{25-8p^{2}}+5}{4}\text{ and }x\geq \frac{-\sqrt{25-8p^{2}}+5}{4}\text{ and }|p|<\frac{5\sqrt{2}}{4}\right)\text{ or }\left(x=\frac{5}{4}\text{ and }|p|\leq \frac{5\sqrt{2}}{4}\right)$$