Solve y=x^2-mx+(m-1)

$$y = x ^ { 2 } - m x + ( m - 1 )$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=-\frac{x^{2}-y-1}{1-x}\text{, }&x\neq 1\\m\in \mathrm{C}\text{, }&y=0\text{ and }x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$x^{2}-mx+m-1=y$$

Subtract x^{2} from both sides.

$$-mx+m-1=y-x^{2}$$

Add 1 to both sides.

$$-mx+m=y-x^{2}+1$$

Combine all terms containing m.

$$\left(-x+1\right)m=y-x^{2}+1$$

The equation is in standard form.

$$\left(1-x\right)m=1+y-x^{2}$$

Divide both sides by -x+1.

$$\frac{\left(1-x\right)m}{1-x}=\frac{1+y-x^{2}}{1-x}$$

Dividing by -x+1 undoes the multiplication by -x+1.

$$m=\frac{1+y-x^{2}}{1-x}$$

Solve for m

$$\left\{\begin{matrix}m=-\frac{x^{2}-y-1}{1-x}\text{, }&x\neq 1\\m\in \mathrm{R}\text{, }&y=0\text{ and }x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$x^{2}-mx+m-1=y$$

Subtract x^{2} from both sides.

$$-mx+m-1=y-x^{2}$$

Add 1 to both sides.

$$-mx+m=y-x^{2}+1$$

Combine all terms containing m.

$$\left(-x+1\right)m=y-x^{2}+1$$

The equation is in standard form.

$$\left(1-x\right)m=1+y-x^{2}$$

Divide both sides by -x+1.

$$\frac{\left(1-x\right)m}{1-x}=\frac{1+y-x^{2}}{1-x}$$

Dividing by -x+1 undoes the multiplication by -x+1.

$$m=\frac{1+y-x^{2}}{1-x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{4y+m^{2}-4m+4}+m}{2}$$

$$x=\frac{-\sqrt{4y+m^{2}-4m+4}+m}{2}$$

Solve for x

$$x=\frac{\sqrt{4y+m^{2}-4m+4}+m}{2}$$

$$x=\frac{-\sqrt{4y+m^{2}-4m+4}+m}{2}\text{, }y\geq -\frac{\left(m-2\right)^{2}}{4}$$