Solve -0.5x+2=-0.5x^2+yx+z

$$-0.5x+2=-0.5 { x }^{ 2 } +yx+z$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=\frac{x^{2}-x-2z+4}{2x}\text{, }&x\neq 0\\y\in \mathrm{C}\text{, }&z=2\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$-0.5x^{2}+yx+z=-0.5x+2$$

Add 0.5x^{2} to both sides.

$$yx+z=-0.5x+2+0.5x^{2}$$

Subtract z from both sides.

$$yx=-0.5x+2+0.5x^{2}-z$$

The equation is in standard form.

$$xy=\frac{x^{2}}{2}-\frac{x}{2}-z+2$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{\frac{x^{2}}{2}-\frac{x}{2}-z+2}{x}$$

Dividing by x undoes the multiplication by x.

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

Divide -\frac{x}{2}+2+\frac{x^{2}}{2}-z by x.

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

Solve for y

$$\left\{\begin{matrix}y=\frac{x^{2}-x-2z+4}{2x}\text{, }&x\neq 0\\y\in \mathrm{R}\text{, }&z=2\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$-0.5x^{2}+yx+z=-0.5x+2$$

Add 0.5x^{2} to both sides.

$$yx+z=-0.5x+2+0.5x^{2}$$

Subtract z from both sides.

$$yx=-0.5x+2+0.5x^{2}-z$$

The equation is in standard form.

$$xy=\frac{x^{2}}{2}-\frac{x}{2}-z+2$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{\frac{x^{2}}{2}-\frac{x}{2}-z+2}{x}$$

Dividing by x undoes the multiplication by x.

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

Divide -\frac{x}{2}+2+\frac{x^{2}}{2}-z by x.

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

Solve for x (complex solution)

$$x=\sqrt{y^{2}+y+2z-3.75}+y+0.5$$

$$x=-\sqrt{y^{2}+y+2z-3.75}+y+0.5$$

Solve for x

$$x=\sqrt{y^{2}+y+2z-3.75}+y+0.5$$

$$x=-\sqrt{y^{2}+y+2z-3.75}+y+0.5\text{, }z\geq -\frac{y^{2}}{2}-\frac{y}{2}+\frac{15}{8}$$