Solve x^y-dx-k=0

$$x ^ { y } - d x - k = 0$$

Solve for d (complex solution)

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

Steps for Solving Linear Equation

Subtract x^{y} from both sides. Anything subtracted from zero gives its negation.

$$-dx-k=-x^{y}$$

Add k to both sides.

$$-dx=-x^{y}+k$$

The equation is in standard form.

$$\left(-x\right)d=k-x^{y}$$

Divide both sides by -x.

$$\frac{\left(-x\right)d}{-x}=\frac{k-x^{y}}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$d=\frac{k-x^{y}}{-x}$$

Divide k-x^{y} by -x.

$$d=-\frac{k-x^{y}}{x}$$

Solve for k (complex solution)

$$k=x^{y}-dx$$

Steps for Solving Linear Equation

Subtract x^{y} from both sides. Anything subtracted from zero gives its negation.

$$-dx-k=-x^{y}$$

Add dx to both sides.

$$-k=-x^{y}+dx$$

The equation is in standard form.

$$-k=dx-x^{y}$$

Divide both sides by -1.

$$\frac{-k}{-1}=\frac{dx-x^{y}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$k=\frac{dx-x^{y}}{-1}$$

Divide -x^{y}+dx by -1.

$$k=x^{y}-dx$$

Solve for d

$$\left\{\begin{matrix}d=\frac{x^{y}-k}{x}\text{, }&x>0\text{ or }\left(Denominator(y)\text{bmod}2=1\text{ and }x<0\right)\\d\in \mathrm{R}\text{, }&x=0\text{ and }k=0\text{ and }y>0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x^{y} from both sides. Anything subtracted from zero gives its negation.

$$-dx-k=-x^{y}$$

Add k to both sides.

$$-dx=-x^{y}+k$$

The equation is in standard form.

$$\left(-x\right)d=k-x^{y}$$

Divide both sides by -x.

$$\frac{\left(-x\right)d}{-x}=\frac{k-x^{y}}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$d=\frac{k-x^{y}}{-x}$$

Divide k-x^{y} by -x.

$$d=-\frac{k-x^{y}}{x}$$

Solve for k

$$k=x^{y}-dx$$

$$\left(x<0\text{ and }Denominator(y)\text{bmod}2=1\right)\text{ or }\left(x=0\text{ and }y>0\right)\text{ or }x>0$$

Steps for Solving Linear Equation

Subtract x^{y} from both sides. Anything subtracted from zero gives its negation.

$$-dx-k=-x^{y}$$

Add dx to both sides.

$$-k=-x^{y}+dx$$

The equation is in standard form.

$$-k=dx-x^{y}$$

Divide both sides by -1.

$$\frac{-k}{-1}=\frac{dx-x^{y}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$k=\frac{dx-x^{y}}{-1}$$

Divide -x^{y}+dx by -1.

$$k=x^{y}-dx$$