Solve x_1^5=0.25x_{1}70.25x_{2}

$$x _ { 1 } ^ { 5 } = 0.25 x _ { 1 } 70.25 x _ { 2 }$$

Solve for x_2

$$\left\{\begin{matrix}\\x_{2}=\frac{16x_{1}^{4}}{281}\text{, }&\text{unconditionally}\\x_{2}\in \mathrm{R}\text{, }&x_{1}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply 0.25 and 70.25 to get 17.5625.

$$x_{1}^{5}=17.5625x_{1}x_{2}$$

Swap sides so that all variable terms are on the left hand side.

$$17.5625x_{1}x_{2}=x_{1}^{5}$$

The equation is in standard form.

$$\frac{281x_{1}}{16}x_{2}=x_{1}^{5}$$

Divide both sides by 17.5625x_{1}.

$$\frac{16\times \frac{281x_{1}}{16}x_{2}}{281x_{1}}=\frac{16x_{1}^{5}}{281x_{1}}$$

Dividing by 17.5625x_{1} undoes the multiplication by 17.5625x_{1}.

$$x_{2}=\frac{16x_{1}^{5}}{281x_{1}}$$

Divide x_{1}^{5} by 17.5625x_{1}.

$$x_{2}=\frac{16x_{1}^{4}}{281}$$

Solve for x_1

$$\left\{\begin{matrix}\\x_{1}=0\text{, }&\text{unconditionally}\\x_{1}=\frac{\sqrt[4]{281x_{2}}}{2}\text{; }x_{1}=-\frac{\sqrt[4]{281x_{2}}}{2}\text{, }&x_{2}\geq 0\end{matrix}\right.$$