Solve fy=(x-6)^2+2

$$f y = ( x - 6 ) ^ { 2 } + 2$$

Solve for f (complex solution)

$$\left\{\begin{matrix}f=-\frac{-x^{2}+12x-38}{y}\text{, }&y\neq 0\\f\in \mathrm{C}\text{, }&\left(x=6+\sqrt{2}i\text{ or }x=-\sqrt{2}i+6\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-6\right)^{2}.

$$fy=x^{2}-12x+36+2$$

Add 36 and 2 to get 38.

$$fy=x^{2}-12x+38$$

The equation is in standard form.

$$yf=x^{2}-12x+38$$

Divide both sides by y.

$$\frac{yf}{y}=\frac{x^{2}-12x+38}{y}$$

Dividing by y undoes the multiplication by y.

$$f=\frac{x^{2}-12x+38}{y}$$

Solve for f

$$f=-\frac{-x^{2}+12x-38}{y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-6\right)^{2}.

$$fy=x^{2}-12x+36+2$$

Add 36 and 2 to get 38.

$$fy=x^{2}-12x+38$$

The equation is in standard form.

$$yf=x^{2}-12x+38$$

Divide both sides by y.

$$\frac{yf}{y}=\frac{x^{2}-12x+38}{y}$$

Dividing by y undoes the multiplication by y.

$$f=\frac{x^{2}-12x+38}{y}$$

Solve for x (complex solution)

$$x=-\sqrt{fy-2}+6$$

$$x=\sqrt{fy-2}+6$$

Solve for x

$$\left\{\begin{matrix}x=-\sqrt{fy-2}+6\text{; }x=\sqrt{fy-2}+6\text{, }&\left(y<0\text{ and }f\leq \frac{2}{y}\right)\text{ or }\left(y>0\text{ and }f\geq \frac{2}{y}\right)\\x=6\text{, }&f=\frac{2}{y}\text{ and }y\neq 0\end{matrix}\right.$$