Solve y=kx^2-8x-8

$$y = k x ^ { 2 } - 8 x - 8$$

Solve for k (complex solution)

$$\left\{\begin{matrix}k=\frac{8x+y+8}{x^{2}}\text{, }&x\neq 0\\k\in \mathrm{C}\text{, }&y=-8\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$kx^{2}-8x-8=y$$

Add 8x to both sides.

$$kx^{2}-8=y+8x$$

Add 8 to both sides.

$$kx^{2}=y+8x+8$$

The equation is in standard form.

$$x^{2}k=8x+y+8$$

Divide both sides by x^{2}.

$$\frac{x^{2}k}{x^{2}}=\frac{8x+y+8}{x^{2}}$$

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

$$k=\frac{8x+y+8}{x^{2}}$$

Solve for k

$$\left\{\begin{matrix}k=\frac{8x+y+8}{x^{2}}\text{, }&x\neq 0\\k\in \mathrm{R}\text{, }&y=-8\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$kx^{2}-8x-8=y$$

Add 8x to both sides.

$$kx^{2}-8=y+8x$$

Add 8 to both sides.

$$kx^{2}=y+8x+8$$

The equation is in standard form.

$$x^{2}k=8x+y+8$$

Divide both sides by x^{2}.

$$\frac{x^{2}k}{x^{2}}=\frac{8x+y+8}{x^{2}}$$

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

$$k=\frac{8x+y+8}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{ky+8k+16}+4}{k}\text{; }x=\frac{-\sqrt{ky+8k+16}+4}{k}\text{, }&k\neq 0\\x=\frac{-y-8}{8}\text{, }&k=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{ky+8k+16}+4}{k}\text{; }x=\frac{-\sqrt{ky+8k+16}+4}{k}\text{, }&\left(k>0\text{ or }y\leq -\frac{8k+16}{k}\right)\text{ and }\left(y\leq \text{Indeterminate}\text{ or }k\neq 0\right)\text{ and }\left(k<0\text{ or }\left(k\neq 0\text{ and }y\geq -\frac{8k+16}{k}\right)\right)\\x=\frac{-y-8}{8}\text{, }&k=0\end{matrix}\right.$$