Solve mx^2-4x+y^2-4y+22=0

$$m x ^ { 2 } - 4 x + y ^ { 2 } - 4 y + 22 = 0$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=-\frac{22-4y+y^{2}-4x}{x^{2}}\text{, }&x\neq 0\\m\in \mathrm{C}\text{, }&\left(y=-3\sqrt{2}i+2\text{ or }y=2+3\sqrt{2}i\right)\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 4x to both sides. Anything plus zero gives itself.

$$mx^{2}+y^{2}-4y+22=4x$$

Subtract y^{2} from both sides.

$$mx^{2}-4y+22=4x-y^{2}$$

Add 4y to both sides.

$$mx^{2}+22=4x-y^{2}+4y$$

Subtract 22 from both sides.

$$mx^{2}=4x-y^{2}+4y-22$$

The equation is in standard form.

$$x^{2}m=4x-y^{2}+4y-22$$

Divide both sides by x^{2}.

$$\frac{x^{2}m}{x^{2}}=\frac{4x-y^{2}+4y-22}{x^{2}}$$

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

$$m=\frac{4x-y^{2}+4y-22}{x^{2}}$$

Solve for m

$$m=-\frac{22-4y+y^{2}-4x}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Add 4x to both sides. Anything plus zero gives itself.

$$mx^{2}+y^{2}-4y+22=4x$$

Subtract y^{2} from both sides.

$$mx^{2}-4y+22=4x-y^{2}$$

Add 4y to both sides.

$$mx^{2}+22=4x-y^{2}+4y$$

Subtract 22 from both sides.

$$mx^{2}=4x-y^{2}+4y-22$$

The equation is in standard form.

$$x^{2}m=4x-y^{2}+4y-22$$

Divide both sides by x^{2}.

$$\frac{x^{2}m}{x^{2}}=\frac{4x-y^{2}+4y-22}{x^{2}}$$

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

$$m=\frac{4x-y^{2}+4y-22}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{4-22m+4my-my^{2}}+2}{m}\text{; }x=\frac{-\sqrt{4-22m+4my-my^{2}}+2}{m}\text{, }&m\neq 0\\x=\frac{y^{2}-4y+22}{4}\text{, }&m=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{4-22m+4my-my^{2}}+2}{m}\text{; }x=\frac{-\sqrt{4-22m+4my-my^{2}}+2}{m}\text{, }&m\neq 0\text{ and }m\leq -\frac{4}{-y^{2}+4y-22}\\x=\frac{y^{2}-4y+22}{4}\text{, }&m=0\end{matrix}\right.$$