求解 x=450+80t-160sqrt{5t}

$$x = 450 + 80 t - 160 \sqrt { 5 t }$$

求解 t 的值 (复数求解)

$$\left\{\begin{matrix}t=0\text{, }&x=450\\t=\frac{\left(-\sqrt{x-50}+20\right)^{2}}{80}\text{, }&arg(-\frac{\sqrt{5x-250}}{20}+\sqrt{5})<\pi \\t=\frac{\left(\sqrt{x-50}+20\right)^{2}}{80}\text{, }&arg(\frac{\sqrt{5x-250}}{20}+\sqrt{5})<\pi \end{matrix}\right.$$

求解 x 的值 (复数求解)

$$x=80t-160\sqrt{5t}+450$$

求解 t 的值

$$\left\{\begin{matrix}t=\frac{\left(-\sqrt{x-50}+20\right)^{2}}{80}\text{, }&x\geq 50\text{ and }-\frac{\sqrt{5x-250}}{20}+\sqrt{5}\geq 0\\t=\frac{\left(\sqrt{x-50}+20\right)^{2}}{80}\text{, }&x\geq 50\end{matrix}\right.$$

求解 x 的值

$$x=80t-160\sqrt{5t}+450$$

$$t\geq 0$$