Solve y=-sqrt{1-x^2}+bx

$$y = - \sqrt { 1 - x ^ { 2 } } + b x$$

Solve for b (complex solution)

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

Steps for Solving Linear Equation

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

$$-\sqrt{1-x^{2}}+bx=y$$

Add \sqrt{1-x^{2}} to both sides.

$$bx=y+\sqrt{1-x^{2}}$$

The equation is in standard form.

$$xb=\sqrt{1-x^{2}}+y$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{\sqrt{1-x^{2}}+y}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{\sqrt{1-x^{2}}+y}{x}$$

Solve for b

$$\left\{\begin{matrix}b=\frac{\sqrt{1-x^{2}}+y}{x}\text{, }&x\neq 0\text{ and }|x|\leq 1\\b\in \mathrm{R}\text{, }&x=0\text{ and }y=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$-\sqrt{1-x^{2}}+bx=y$$

Add \sqrt{1-x^{2}} to both sides.

$$bx=y+\sqrt{1-x^{2}}$$

The equation is in standard form.

$$xb=\sqrt{1-x^{2}}+y$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{\sqrt{1-x^{2}}+y}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{\sqrt{1-x^{2}}+y}{x}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{-by+\sqrt{1+b^{2}-y^{2}}}{b^{2}+1}\text{; }x=\frac{by+\sqrt{1+b^{2}-y^{2}}}{b^{2}+1}\text{, }&b\neq i\text{ and }b\neq -i\text{ and }arg(y-bx)\geq \pi \\x=\frac{y^{2}-1}{2by}\text{, }&\left(y\neq 0\text{ and }b=i\text{ and }arg(y-ix)\geq \pi \right)\text{ or }\left(y\neq 0\text{ and }b=-i\text{ and }arg(ix+y)\geq \pi \right)\\x=-1\text{, }&y=-b\\x=1\text{, }&y=b\end{matrix}\right.$$