Solve y=k(x^2+1)

$$y = k ( x ^ { 2 } + 1 )$$

Solve for k (complex solution)

$$\left\{\begin{matrix}k=\frac{y}{x^{2}+1}\text{, }&x\neq -i\text{ and }x\neq i\\k\in \mathrm{C}\text{, }&\left(x=i\text{ or }x=-i\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply k by x^{2}+1.

$$y=kx^{2}+k$$

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

$$kx^{2}+k=y$$

Combine all terms containing k.

$$\left(x^{2}+1\right)k=y$$

Divide both sides by x^{2}+1.

$$\frac{\left(x^{2}+1\right)k}{x^{2}+1}=\frac{y}{x^{2}+1}$$

Dividing by x^{2}+1 undoes the multiplication by x^{2}+1.

$$k=\frac{y}{x^{2}+1}$$

Solve for k

$$k=\frac{y}{x^{2}+1}$$

Steps for Solving Linear Equation

Use the distributive property to multiply k by x^{2}+1.

$$y=kx^{2}+k$$

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

$$kx^{2}+k=y$$

Combine all terms containing k.

$$\left(x^{2}+1\right)k=y$$

Divide both sides by x^{2}+1.

$$\frac{\left(x^{2}+1\right)k}{x^{2}+1}=\frac{y}{x^{2}+1}$$

Dividing by x^{2}+1 undoes the multiplication by x^{2}+1.

$$k=\frac{y}{x^{2}+1}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\sqrt{\frac{y}{k}-1}\text{; }x=\sqrt{\frac{y}{k}-1}\text{, }&k\neq 0\\x\in \mathrm{C}\text{, }&y=0\text{ and }k=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\sqrt{\frac{y}{k}-1}\text{; }x=-\sqrt{\frac{y}{k}-1}\text{, }&\left(k<0\text{ or }y\geq k\right)\text{ and }\left(k>0\text{ or }y\leq k\right)\text{ and }k\neq 0\\x\in \mathrm{R}\text{, }&y=0\text{ and }k=0\end{matrix}\right.$$