Solve x^2-2z+8-55=dx-x^2

$$x ^ { 2 } - 2 z + 8 - 55 = d x - x ^ { 2 }$$

Solve for d (complex solution)

$$\left\{\begin{matrix}d=\frac{2x^{2}-2z-47}{x}\text{, }&x\neq 0\\d\in \mathrm{C}\text{, }&z=-\frac{47}{2}\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 55 from 8 to get -47.

$$x^{2}-2z-47=dx-x^{2}$$

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

$$dx-x^{2}=x^{2}-2z-47$$

Add x^{2} to both sides.

$$dx=x^{2}-2z-47+x^{2}$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$dx=2x^{2}-2z-47$$

The equation is in standard form.

$$xd=2x^{2}-2z-47$$

Divide both sides by x.

$$\frac{xd}{x}=\frac{2x^{2}-2z-47}{x}$$

Dividing by x undoes the multiplication by x.

$$d=\frac{2x^{2}-2z-47}{x}$$

Solve for d

$$\left\{\begin{matrix}d=\frac{2x^{2}-2z-47}{x}\text{, }&x\neq 0\\d\in \mathrm{R}\text{, }&z=-\frac{47}{2}\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 55 from 8 to get -47.

$$x^{2}-2z-47=dx-x^{2}$$

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

$$dx-x^{2}=x^{2}-2z-47$$

Add x^{2} to both sides.

$$dx=x^{2}-2z-47+x^{2}$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$dx=2x^{2}-2z-47$$

The equation is in standard form.

$$xd=2x^{2}-2z-47$$

Divide both sides by x.

$$\frac{xd}{x}=\frac{2x^{2}-2z-47}{x}$$

Dividing by x undoes the multiplication by x.

$$d=\frac{2x^{2}-2z-47}{x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{16z+d^{2}+376}+d}{4}$$

$$x=\frac{-\sqrt{16z+d^{2}+376}+d}{4}$$

Solve for x

$$x=\frac{\sqrt{16z+d^{2}+376}+d}{4}$$

$$x=\frac{-\sqrt{16z+d^{2}+376}+d}{4}\text{, }z\geq -\frac{d^{2}}{16}-\frac{47}{2}$$