Solve f(x)=x-x^2quadx_{0}=1

$$f ( x ) = x - x ^ { 2 } \quad x _ { 0 } = 1$$

Solve for x_0

$$x_{0}=\frac{x-1}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract x from both sides.

$$-x^{2}x_{0}=1-x$$

The equation is in standard form.

$$\left(-x^{2}\right)x_{0}=1-x$$

Divide both sides by -x^{2}.

$$\frac{\left(-x^{2}\right)x_{0}}{-x^{2}}=\frac{1-x}{-x^{2}}$$

Dividing by -x^{2} undoes the multiplication by -x^{2}.

$$x_{0}=\frac{1-x}{-x^{2}}$$

Divide 1-x by -x^{2}.

$$x_{0}=\frac{x-1}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{\sqrt{1-4x_{0}}-1}{2x_{0}}\text{; }x=\frac{\sqrt{1-4x_{0}}+1}{2x_{0}}\text{, }&x_{0}\neq 0\\x=1\text{, }&x_{0}=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{\sqrt{1-4x_{0}}-1}{2x_{0}}\text{; }x=\frac{\sqrt{1-4x_{0}}+1}{2x_{0}}\text{, }&x_{0}\neq 0\text{ and }x_{0}\leq \frac{1}{4}\\x=1\text{, }&x_{0}=0\end{matrix}\right.$$