Solve y^2=c_{1}x+c_{2}

$$y ^ { 2 } = c _ { 1 } x + c _ { 2 }$$

Solve for c_1 (complex solution)

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

Steps for Solving Linear Equation

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

$$c_{1}x+c_{2}=y^{2}$$

Subtract c_{2} from both sides.

$$c_{1}x=y^{2}-c_{2}$$

The equation is in standard form.

$$xc_{1}=y^{2}-c_{2}$$

Divide both sides by x.

$$\frac{xc_{1}}{x}=\frac{y^{2}-c_{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$c_{1}=\frac{y^{2}-c_{2}}{x}$$

Solve for c_1

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

Steps for Solving Linear Equation

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

$$c_{1}x+c_{2}=y^{2}$$

Subtract c_{2} from both sides.

$$c_{1}x=y^{2}-c_{2}$$

The equation is in standard form.

$$xc_{1}=y^{2}-c_{2}$$

Divide both sides by x.

$$\frac{xc_{1}}{x}=\frac{y^{2}-c_{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$c_{1}=\frac{y^{2}-c_{2}}{x}$$

Solve for c_2

$$c_{2}=y^{2}-c_{1}x$$

Solution Steps

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

$$c_{1}x+c_{2}=y^{2}$$

Subtract c_{1}x from both sides.

$$c_{2}=y^{2}-c_{1}x$$