Solve z=x^2+y^2+1/5(x+2y-16)^2

$$z = x ^ { 2 } + y ^ { 2 } + \frac { 1 } { 5 } ( x + 2 y - 16 ) ^ { 2 }$$

Solve for x (complex solution)

$$x=\frac{\sqrt{-50y^{2}+320y+30z-1280}}{6}-\frac{y}{3}+\frac{8}{3}$$

$$x=-\frac{\sqrt{-50y^{2}+320y+30z-1280}}{6}-\frac{y}{3}+\frac{8}{3}$$

Solve for y (complex solution)

$$y=\frac{\sqrt{-50x^{2}+160x+45z-1280}-2x+32}{9}$$

$$y=\frac{-\sqrt{-50x^{2}+160x+45z-1280}-2x+32}{9}$$

Solve for x

$$x=\frac{\sqrt{-50y^{2}+320y+30z-1280}}{6}-\frac{y}{3}+\frac{8}{3}$$

$$x=-\frac{\sqrt{-50y^{2}+320y+30z-1280}}{6}-\frac{y}{3}+\frac{8}{3}\text{, }z\geq \frac{5y^{2}-32y+128}{3}$$

Solve for y

$$y=\frac{\sqrt{-50x^{2}+160x+45z-1280}-2x+32}{9}$$

$$y=\frac{-\sqrt{-50x^{2}+160x+45z-1280}-2x+32}{9}\text{, }z\geq \frac{10x^{2}-32x+256}{9}$$